diff --git "a/3tE1T4oBgHgl3EQfSQPo/content/tmp_files/load_file.txt" "b/3tE1T4oBgHgl3EQfSQPo/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/3tE1T4oBgHgl3EQfSQPo/content/tmp_files/load_file.txt" @@ -0,0 +1,890 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf,len=889 +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (0000) 000: DOI Probing Cosmology beyond ΛCDM using the SKA Shamik Ghosh1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Pankaj Jain3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Rahul Kothari4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='*,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Mohit Panwar3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Gurmeet Singh3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Prabhakar Tiwari5 1CAS Key Laboratory for Researches in Galaxies and Cosmology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' University of Science and Technology of China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Hefei,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Anhui 230026,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' China 2School of Astronomy and Space Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' University of Science and Technology of China,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Hefei,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 230026,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' China 3Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Indian Institute of Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Kanpur-208016,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 4Department of Physics & Astronomy, University of the Western Cape, Cape Town 7535, South Africa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 5National Astronomical Observatories, Chinese Academy of Science, Beijing 100101, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' E-mail: quantummechanicskothari@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='com MS received 1 January 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' accepted 1 January 2022 Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The cosmological principle states that the Universe is statistically homogeneous and isotropic at large distance scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' There currently exist many observations which indicate a departure from this principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It has been shown that many of these observations can be explained by invoking superhorizon cosmological perturbations and may be consistent with the Big Bang paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Remarkably, these modes simultaneously explain the observed Hubble tension, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', the discrepancy between the direct and indirect measurements of the Hubble parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We propose several tests of the cosmological principle using SKA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In particular, we can reliably extract the signal of dipole anisotropy in the distribution of radio galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The superhorizon perturbations also predict a significant redshift dependence of the dipole signal which can be nicely tested by the study of signals of reionization and the dark ages using SKA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We also propose to study the alignment of radio galaxy axes as well as their integrated polarization vectors over distance scales ranging from a few Mpc to Gpc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We discuss data analysis techniques that can reliably extract these signals from data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' cosmological principle—superhorizon perturbations—square kilometre array.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Introduction Current observations support an expanding universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' If we extrapolate this back in time, we can infer that the Universe started from a very hot and dense state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This event, known as Big Bang, marked the origin of the Universe in a very high temperature state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In order to make the problem of expansion dynam- ics tractable, we assume that the Universe is spatially isotropic and homogeneous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This assumption is also known as Cosmological Principle (hereafter CP) (Kolb & Turner, 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Einstein, 1917;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Aluri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It turns out that Hubble’s law is a direct consequence of CP (Coles & Lucchin, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Furthermore, it can be shown that the most general spacetime metric that de- scribes a universe following CP is the FLRW metric (Weinberg, 1972;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Coles & Lucchin, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It is also im- portant to mention that CP is an independent assump- tion and does not follow from symmetries of the Ein- stein’s Equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The FLRW metric describes a Universe with a smooth background having an exact isotropic and ho- mogeneous matter distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' But observationally, the Universe also possesses structure in the form of stars, galaxies, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These structures arise due to cur- vature perturbations which are seeded during the epoch of exponential expansion called inflation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The resulting cosmological model, including dark matter and dark energy is called ΛCDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Although, these perturbations aren’t isotropic and homogeneous per se, they satisfy these properties in a statistical sense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For example, in the cosmic frame of rest, the matter density is expected to be the same at all points provided we average over a sufficiently large distance scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The precise value of this distance scale is still not clear but is expected to be of order 100 Mpc (see, for example Kim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2021)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It has been speculated that during an epoch, be- fore inflation ensued, the Universe may be described by a complicated metric whose nature is currently poorly understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' However, it quickly evolves to the isotropic and homogeneous FLRW metric during infla- © Indian Academy of Sciences 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='03065v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='CO] 8 Jan 2023 Page 2 of J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (0000) 000: tion, perhaps within the first e-fold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Wald (1983) for the first time, gave an explicit demonstration for Bianchi Universes (except type IX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Some other results also exist for inhomogeneous metric (Stein-Schabes, 1987;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Jensen & Stein-Schabes, 1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We may speculate that the idea generalizes to a larger class of metrics1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The Big Bang paradigm is therefore consistent with an early anisotropic and/or inhomogeneous phase of the Uni- verse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Given the existence of such a phase, it is clearly important to ask whether it has any observational con- sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Observationally, the Universe is found to be consis- tent with CP to a good approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' But currently there exist many observations in CMB and large scale structures (LSS henceforth) which appear to violate CP (Ghosh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We review these anomalies later in §2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For an expansive review, see Aluri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' There exist many theoretical attempts to explain these observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It has been suggested that superhorizon modes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', perturbations of wavelengths larger than the horizon size (Grishchuk & Zeldovich, 1978a,b), may explain some of these observations (Gordon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Erickcek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2008a,b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Ghosh, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Additionally, these can ac- count for low-ℓ alignments (Gao, 2011), though these can’t extenuate the present accelerated expansion of the Universe (Hirata & Seljak, 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Flanagan, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It is assumed that such large wavelength modes are aligned with one another and hence do not obey CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' An intriguing possibility is that such modes might orig- inate during an anisotropic and/or inhomogeneous pre- inflationary phase of the Universe (Aluri & Jain, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Rath et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Hence, despite being in violation with CP, they would be consistent with the Big Bang paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1 Mathematical Formulation and Ramifications In order to relate theory with observations, we seek en- semble averages of the fields under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Er- godicity hypothesis (Ellis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2012) allows us to re- late this ensemble averaging to the space averaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It is known that for the gaussian random fields, all the statistical information is contained in the 2 point cor- relation functions (2PCF).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' However, in the presence of non-gaussianities, we need higher order correlators like bispectrum (3PCF) or trispectrum (4PCF), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', in or- der to extract optimal cosmological information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' CP dictates that the nPCF only be a function of distances between the points xi ≡ (zi, ni).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Thus �ρ(x1)ρ(x2) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' ρ(xn)� = f(x12, x13, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' , xi j, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' ), (1) 1There are exceptions to these results as well (Sato, 1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' A O C B Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Illustration of statistical isotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In this Figure, A, B and C are given points on the spherical surface such that ∠AOB = ∠AOC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' where xij = |xi − xj| = xji and i � j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Clearly, this makes this nPCF invariant under arbitrary translations and rotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The condition (1) for 2PCF in case of a 2D field, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', CMB temperature, takes the usual form �T(x1)T(x2)� ≡ �T( ˆm)T(ˆn)� = f( ˆm · ˆn), (2) with x1 ≡ (z∗, ˆn) and x2 ≡ (z∗, ˆm), z∗ being the red- shift to decoupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2) is the familiar result for the 2PCF, which dictates that the temperature correla- tion depends only upon the angle between the locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This is illustrated in Figure 1, where three points A, B and C are chosen in a manner such that ∠AOC = ∠AOB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Thus we must have �T(A)T(C)� = �T(A)T(B)�, since A · C = A · B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Observations at tension with ΛCDM Our observations in the past two decades have firmly planted the inflationary ΛCDM cosmology as the stan- dard paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' A vast set of observables from CMB to LSS broadly agree with ΛCDM predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Despite the successes of ΛCDM, we have a growing set of ob- servations that are at tension with our expectations from ΛCDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We will summarise some of the observed ten- sions, in the context of the model discussed in this pa- per.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' See Perivolaropoulos & Skara (2022) for a review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1 Observed violations of Statistical Isotropy As we discussed before, CP implies statistical isotropy and homogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Due to our fixed vantage point, it is not possible to directly test statistical homogene- ity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' However, we can test statistical isotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Various J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (0000)000: Page 3 of observational tests, performed on different cosmologi- cal datasets, amply attest statistical isotropy violations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Some of these are reviewed in Ghosh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1 The kinematic dipole: As explained in the §1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', CP is valid only in the cosmic frame of rest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We as ob- servers are not stationary with respect to this frame on account of the motion of Earth, the Sun, and the Milky Way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This gives rise to an effective peculiar velocity to our observation frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This peculiar velocity results in a Doppler boost of the CMB temperature fluctuation, further culminating in a kinematic dipole in the CMB temperature fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Interpreting the CMB dipole to be of kinematic origin (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2014) leads to the peculiar velocity of our local frame to be 384 ± 78 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The peculiar velocity v of our observation is ex- pected to give rise to a dipole in the observed num- ber count of sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The local motion would cause a Doppler and aberration effects, both of which con- tribute to a dipole in the observed number counts (Ellis & Baldwin, 1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For sources with flux following a power law relation in frequency: S ∝ ν−α, and with dif- ferential number count N(S, ˆn) = S −1−x, the expected dipole is given by: D = [2 + x(1 + α)] v/c, (3) where c is the speed of light, α is the frequency scal- ing spectral index, and (1 + x) is the slope of ln N v/s − ln S plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We can use the estimates of our peculiar velocity from the CMB and use it to predict the esti- mated dipole in the large-scale structure data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Assum- ing α ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='75 and x ≈ 1, we find the expected dipole Dth ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Measurements of the dipole in LSS sur- veys at z ∼ 1 have all yielded results that are consis- tent with CMB direction but the magnitude is found to be double or more of the predicted value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In Table 1, we list the measured value of dipole in the NVSS, NVSS+WENSS, NVSS+SUMSS and CatWISE cata- logs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The dipole measured in the LSS has a much larger magnitude than expected from CMB measurements but is consistent with the CMB dipole direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The devia- tion is found to be at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='9σ in the CatWISE data (Secrest et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We point out that the assumed power law depen- dence of number counts on S is not strictly valid (Ti- wari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This leads to a difference in the dipole in number counts and in sky brightness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It also introduces a dipole in the mean flux per source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Hence this provides a nontrivial test of whether the dipole is indeed of kinematic origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This idea has been gener- alised in Nadolny et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2021) who develop a method to extract kinematic dipole independently from an in- trinsic dipole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Authors |D| (×10−2) (l, b) Singal (2011) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='3 (239◦, 44◦) Rubart & Schwarz (2013) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='6 (241◦, 39◦) Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2015) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='25 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='40 (261◦, 37◦) Tiwari & Nusser (2016) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='9 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='4 (246◦, 38◦) Colin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2017) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='6 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='2 (241◦, 28◦) Secrest et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2021) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='5 (238◦, 29◦) Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Results for the dipole in LSS exceed the expected value of 5 × 10−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='2 Alignment of quadrupole (ℓ = 2) and octupole (ℓ = 3): Both ℓ = 2, 3 CMB multipoles are aligned with preferred direction pointing roughly along the CMB dipole (de Oliveira-Costa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Physi- cally, both of these multipoles form a planar structure, such that the perpendicular to this plane is aligned with the CMB dipole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='3 Alignment of galaxy axes and polarizations: There have been many observations, both in optical (Hutsem´ekers, 1998) and radio (Tiwari & Jain, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Taylor & Jagannathan, 2016) data sets that suggest alignment of galaxy axes and integrated linear polar- izations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These observations can be nicely explained in terms of the correlated magnetic field which may be of primordial origin (Tiwari & Jain, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Intriguingly, the optical alignment is seen to be very prominent in the direction of the CMB dipole (Ralston & Jain, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='4 Dipole in radio polarization offset angles: The integrated polarizations of radio galaxies are known to be aligned approximately perpendicular to the galaxy position axes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Remarkably, the angle between these two axes shows a dipole pattern in the sky with pre- ferred axis again pointing roughly along the CMB dipole (Jain & Ralston, 1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Hence, we see that sev- eral diverse observations appear to indicate the same preferred direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Taken together, they are strongly suggestive of a violation of the CP (Ralston & Jain, 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='5 Dipole modulation and the Hemispherical Asym- metry: We find that the CMB temperature fluctua- tions have slightly higher power in the southern ecliptic hemisphere than the northern one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This is called the hemispherical power asymmetry and was first observed in the WMAP data (Hoftuft et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2009) and continues to persist in the Planck measurements (Planck Collab- oration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It is also observed that the CMB temperature fluctuations appear to be modulated by a Page 4 of J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (0000) 000: dipole that points close to the south ecliptic pole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This implies that the CMB temperature fluctuation along line-of-sight direction ˆn is given by: ∆T(ˆn) = ∆Tiso [1 + Aλ · ˆn] , (4) where ∆Tiso satisfies CP, A is the amplitude of the dipole and λ is the preferred direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Current Planck measurements (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2020) give A = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='070+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='032 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='015 and λ = (221◦, −21◦) ± 31◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Such a dipole modulation would lead to difference in powers in the two hemispheres along ˆλ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='6 Other CMB observations: Other observations of SI violations in the CMB are low in significance, albeit they are present in both WMAP and Planck data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For low-ℓ values, the even multipoles are anomalously smaller than the odd multipole modes in power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This is called the parity asymmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The largest asymme- try are evidenced in the lowest multipoles, viz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', ℓ ∈ [2, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These low multipoles show an anomalously small power, which is called the low power on large scales in the CMB temperature fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='2 Hubble Tension The Hubble tension is the disagreement in measured value of the Hubble parameter H0 from different meth- ods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The local universe measurements of H0 using the ‘distance ladder’ method with Cepheids and super- novae type Ia (SNIa) or strong lensing systems dif- fer from the measurements from the CMB assuming ΛCDM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Other methods like tip of the red giant branch (TRGB) (Reid et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2019) or gravitational wave events (Gayathri et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Mukherjee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2020) have measured value somewhere between the two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Broadly speaking, H0 measurements from the local universe is larger than the measurements from the CMB at nearly 5σ significance (Anchordoqui & Perez Bergli- affa, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The Cepheid-SNIa measurements use Cepheid variables in host galaxies of SNIa, to calibrate the dis- tance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These calibrated type Ia supernovae are then used to calibrate magnitude and redshift of a large sample of SNIa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The full sample of SNIa probes the Hubble flow and is used to directly infer the Hub- ble parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Riess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2019) estimate the value H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='03 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='42 kms−1Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This agrees with the Freedman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2012) estimate of H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='3 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1 kms−1Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The H0LiCOW team’s (Wong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2020) recent measurement, using the time delay for a system of six gravitationally lensed quasars, yields H0 = 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='3+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='7 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='8 kms−1Mpc−1 that agrees very well with Cepheid (Freedman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2001) measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In addition to the aforementioned ‘direct’ measure- ments, CMB can also be used to infer the value of the Hubble parameter ‘indirectly’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The CMB T and E mode measurements are used to fit the ΛCDM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In its basic form, ΛCDM has only six parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The Hubble parameter can be estimated indirectly from the best fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This indirect estimation of the H0 gives a value lower than the direct measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Planck Collabora- tion et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2018) gives H0 = 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='27 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='60 kms−1Mpc−1 using only T and E mode data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Estimates of H0 us- ing other CMB experiments like ACT (Dunkley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2011) and SPTpol (for ℓ < 1000) (Henning et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2018) give consistent results with Planck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Superhorizon perturbation model It has been suggested that the superhorizon perturba- tions can explain the observed violations of statisti- cal isotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These are perturbations with wavelengths larger than the particle horizon (Erickcek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2008a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Such modes necessarily exist in a cosmological model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' However, in order to explain the the observed viola- tions of isotropy (Gordon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2005) we also need them to be aligned with one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In Gordon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2005), such an alignment is attributed to a stochas- tic phenomenon known as spontaneous breakdown of isotropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Alternatively, the alignment may be attributed to an intrinsic violation of the cosmological principle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' A very interesting possibility is presented in Aluri & Jain (2012) and Rath et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It is argued that during its very early phase, the Universe may not be isotropic and homogeneous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' As explained in §1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', it ac- quires this property during inflation (Wald, 1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The modes which originate during the early phase of in- flation when the Universe deviates from isotropy and homogeneity may not obey the cosmological principle (Rath et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We postulate that these are the aligned superhorizon modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1 Resolution of various anomalies Cosmological implications of this phenomenon have been obtained by assuming the existence of a single adiabatic mode (Erickcek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2008a,b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Ghosh, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Working in the conformal Newtonian Gauge, such a mode can be ex- pressed as, Ψp = ϱ sin(κx3 + ω) (5) Thus a superhorizon mode is characterised by its am- plitude ϱ, wavenumber κ and phase factor ω � 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (5), we have taken the mode to be aligned along the x3 (or z) axis which we also assume to be the direc- tion of CMB dipole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For a superhorizon mode, we have J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (0000)000: Page 5 of κ/H0 ≪ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It has been shown that such a superhorizon mode is consistent with all existing cosmological observations (like CMB, NVSS constraints etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=') for a range of pa- rameters (Ghosh, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Some parameter values are given in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It can affect the large scale distribution of matter and can potentially explain the enigmatic excess dipole sig- nal observed in the radio galaxy distribution (Singal, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Gibelyou & Huterer, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Rubart & Schwarz, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Tiwari & Jain, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Tiwari & Nusser, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Colin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The observed matter dipole, Dobs is expressed as: Dobs = �Dkin + Dgrav + Dint �ˆx3, (6) where Dkin, Dgrav and Dint respectively denote the am- plitudes of the kinematic, gravitational and intrinsic dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These components are redshift dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Thus we can write the magnitude of the observed dipole between the redshifts z1 and z2, due to the superhorizon mode (5) as Dobs(z1, z2) = � A1(z1, z2) + A2(z1, z2) + C(z1, z2) �ϱκ cos ω H0 + B (7) where the term B = [2 + x(1 + α)]v c (8) is the redshift independent kinematic dipole compo- nent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The explicit expressions for other redshift depen- dent factors A1(z1, z2), A2(z1, z2), C(z1, z2) are given in (Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Notice that in the absence of a su- perhorizon mode, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', ϱ → 0, the dipole magnitude in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (7), as expected, becomes redshift independent and equal to (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1 The Matter Dipole: Due to the presence of an aligned superhorizon mode, an additional contribution to our velocity arises with respect to LSS in the CMB dipole direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This is given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='12) of (Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Hence it leads to a change in Dkin in com- parison to its prediction based on CMB dipole (Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Furthermore, the superhorizon mode contributes through the Sachs-Wolfe (SW) and the in- tegrated Sachs-Wolfe (ISW) effects (Erickcek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2008a), thereby leading to Dgrav in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Finally, the superhorizon mode leads to an intrinsic anisotropy in the matter distribution and hence contributes to Dint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (7) is the explicit expression considering all these effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' From the equation, it is clear that for a given value of ϱ > 0, the dipole contribution is maximum if ω = π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' All the contributions due to the mode depend on redshift since the mode has a systematic dependence on distance and hence the predicted dipole is redshift de- pendent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It is interesting to note that the contributions of the superhorizon mode to the CMB dipole cancel out at the leading order (Erickcek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2008a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Such a can- cellation does not happen in the case of matter dipole (Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We may understand this as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' As per Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (6), there are three different contributions to the matter dipole – (a) the kinematic dipole which arises due to our velocity relative to the source, (b) the gravitational dipole (SW and ISW) and (c) the intrin- sic dipole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In the case of CMB, these three add up to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In the case of matter dipole, the kinematic dipole explicitly depends on the parameter α which arises in the spectral dependence of the flux from a source, as well as the parameter x (see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (8)) which arises in the number count distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Furthermore, the gravi- tational effect also depends on α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The intrinsic dipole, however, does not depend on either of these parame- ters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We point out that both of these parameters arise at non-linear order in the theory of structure formation and furthermore the assumed power law distribution is only an approximation (Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These pa- rameters are best extracted from observations and can- not be reliably deduced theoretically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Hence, the sit- uation is very different in the case of matter dipole in comparison to CMB dipole and we do not expect that the two would behave in the same manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We clar- ify that in the case of matter dipole, the superhorizon perturbation is treated at first order in perturbation the- ory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' However, the small wavelength modes which are responsible for structure formation have to be treated at nonlinear order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2021), the existence of structures is assumed as given with their properties de- duced observationally and the calculation focuses only on the additional contribution due to the superhorizon mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' However, a complete first principles calculation would have to treat small wavelength modes at nonlin- ear order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' There are some further issues, associated with gauge invariance (Challinor & Lewis, 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Bonvin & Durrer, 2011), which are not addressed in Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These issues are very important, but to the best of our understanding, they are expected to lead to small corrections to the calculational framework used in Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2021) and not expected to qualitatively change their results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It will be very interesting to repeat these calculations using the gauge invariant framework, but this is beyond the scope of the present paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Such a calculation must also take into account the fact that the aligned superhorizon modes we are considering do not arise within the ΛCDM model but perhaps due to an Page 6 of J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (0000) 000: anisotropic/inhomogeneous early phase of cosmic ex- pansion (Aluri & Jain, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Rath et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='2 Alignment of Quadrupole and Octupole: Fur- ther, the superhorizon mode can also explain the align- ment of CMB quadrupole and octupole (Gordon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' With x3 axis along the CMB dipole, it leads to non-zero spherical harmonic coefficients T10, T20, T30 in the temperature anisotropy field (Erickcek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2008a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We obtain constraints on the mode param- eters in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (5) by requiring that T20 and T30 are less than three times the measured rms values of the quadrupole and octupole powers respectively (Erickcek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2008a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' It turns out that the dipole contribution does not lead to a significant constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These con- tributions can explain the alignment of quadrupole and octupole if we assume the presence of an intrinsic con- tribution to T10 and T20 which is partially cancelled by the contribution due to the superhorizon mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Note that this intrinsic contribution is statistical in nature and hence its exact value cannot be predicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='3 Hubble Tension: It has been shown by Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2021) that a superhorizon mode leads to a per- turbation in the gravitational potential between distant galaxies and us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This culminates in a correction in ob- served redshift of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 1 + zobs = (1 + z)(1 + zDoppler)(1 + zgrav) (9) Thus we see that in the presence of superhorizon modes, the galaxy at redshift z is observed instead at a redshift zobs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In the above equation, the redshifts zDoppler and zgrav are respectively due to our velocity relative to LSS and perturbation in potential introduced by the su- perhorizon mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We can express zobs as (Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022), zobs = ¯z + γ cos θ + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (10) where the first and the second terms on the RHS are the monopole and dipole terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Here θ is the polar angle of the source with x3 axis along the CMB dipole and γ the dipole amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Interestingly, the monopole term in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (10) resolves the Hubble tension (Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For that we need to choose the phase ω � π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The range of parameters which explain both the matter dipole and the Hubble tension is given in (Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In Table 2, we quote some of those values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The superhorizon modes are also likely to leave their signatures in other cosmological observables like Baryon Acoustic Oscillations, epoch of reionziation etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' ω ϱ κ/H0 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='81π 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='97 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='58 × 10−3 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='81π 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='48 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='4 × 10−3 Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Some parameter values for the superhorizon mode (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 5) explaining NVSS excess dipole and also resolving the Hubble tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These values also satisfying CMB constraints are taken from Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Constraints using SKA 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1 Superhorizon perturbation observation The superhorizon model predicts several observations which can be tested with SKA and other future surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' An interesting feature is the significant dependence of dipole on the redshift in the presence of superhorizon modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Hence, the dipole measurements in redshift bins with SKA1 and SKA2 continuum survey can work as a potential test of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For a radio contin- uum survey, it is unlikely that we would have spec- troscopic redshift information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In the past, redshifts of radio galaxies have been estimated by taking cross correlation with well known redshift surveys (Blake & Wall, 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Such strategies are still viable by using data from the GAMA survey fields (Baldry et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' However, new techniques like template fitting (Duncan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2018) or machine learn- ing based photometric redshift computations (Brescia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2021) make it possible for the SKA radio con- tinuum survey galaxies to contain redshift information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This added information provides a unique possibility to test superhorizon mode physics with the SKA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='2 Predictions Here, we demonstrate how precisely evident the dipole predictions with a superhorizon model would be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Fur- ther, we demonstrate how much they are constrained using SKA observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Assuming superhorizon modes that (a) satisfy the present NVSS and Hubble pa- rameter measurements and (b) are consistent with CMB and other cosmological measurements (see Table 2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' we obtain the dipole magnitude Dobs in redshift bins using the formalism described in (Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The dependence of dipole signal on the redshift z is shown in Figure 2 where we have shown the redshift dependence of Dobs for two cases 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Cumulative Redshift Bins: For this case, we fix z1 = 0 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (7) and vary z2 = z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In other words, we calculate Dobs(0, z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Non-overlapping Redshift Bins: In this case, we obtain the non overlapping z dependence by eval- J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (0000)000: Page 7 of 1 2 3 4 5 6 z 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='011 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='013 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='014 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='016 Dobs cumulative redshift bins non-overlapping redshift bins Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The dipole signal observation in the presence of superhorizon modes with SKA1 (z ≤ 5) and SKA2 (z ≤ 6) continuum surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The inner and outer shaded regions respectively represent the optimistic and realistic uncer- tainties for both SKA1 & SKA2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Here we have assumed a superhorizon mode (Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022) satisfying present NVSS dipole observation (Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Flux Density SKA1 SKA2 Optimistic > 10 > 1 Realistic > 20 > 5 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Optimistic and realistic flux densities (in µJy) for SKA1 and SKA2 surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' uating Dobs(z − ∆z, z + ∆z) with ∆z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For a fix ∆z, this thus gives Dobs at z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='3 Estimating Uncertainties We employ Alonso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2015) ‘Ultra-large scales’ codes2 (for continuum surveys) to determine the num- ber densities for SKA surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We further assume that SKA1 and SKA2 will observe the sky up to respective declinations of 15◦ and 30◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The optimistic and realis- tic flux densities’ limits for SKA1 and SKA2 (Square Kilometre Array Cosmology Science Working Group et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Bengaly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2018) are given in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Additionally, we note that SKA1 is expected to probe up to 0 ≤ z ≤ 5, whereas the SKA2 will reach up to redshift 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We mock SKA1 and SKA2 contin- uum sky to determine the observational implications of the superhorizon model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We produce 1000 num- ber density simulation of SKA1 and SKA2 continuum survey for each (optimistic and realistic) flux thresh- old using HEALPix software (Go´rski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2005), with Nside = 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The mean number of galaxies in 2http://intensitymapping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='ox.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='uk/codes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='html a pixel is determined using number density obtained from Alonso et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (2015) code and by modelling a dipole with magnitude and direction expected in pres- ence of a superhorizon mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Given the mean number density in a pixel, we call random Poisson distribution to emulate the galaxy count in the pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The galaxy mock thus neglects the cosmological galaxy clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This is justified since the clustering dipole in LSS is ≈ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='7×10−3 (Nusser & Tiwari, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Tiwari & Nusser, 2016), which is roughly five times less than the appar- ent dipole in LSS3 and inconsequential for our simula- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' This is roughly equal to the uncertainties in the measured dipole is LSS using NVSS galaxies (see Ta- ble 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We consider SKA1, SKA2 sky coverage, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', mask declination above 15◦ and 30◦, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Ad- ditionally, we mask the galactic latitudes (|b| < 10◦) in order to remove Milky Way contamination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The galac- tic plane cut is often chosen to be anywhere between |b| < 5◦ and |b| < 15◦, and in most studies one tests the robustness of the results with varying redshift cuts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For tests on mock data, here we choose a typical cut of |b| < 10◦ that should balance the exclusion of galac- tic plane contamination and loss of sky fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Next, we use Python Healpy4 (Go´rski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Zonca et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2019) fit dipole function and obtain dipole for each 1000 mock maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' From these 1000 dipole val- ues, we calculate the standard deviation to determine the uncertainty in measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The shaded regions in Figure 2 show the results obtained for SKA1 and SKA2 optimistic and realistic number densities in non- overlapping and cumulative redshift bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='4 Other Anisotropy tests with SKA If the universe does not follow CP at large distance scales then every observable should have directional dependence characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Out of all, three observ- ables are of particular interest as these are independent of the number density over the sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' So these are more robust under unequal coverage and systematics of the sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These observables are Mean spectral index (¯α) – As we said in §2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='1, the spectral index for a radio source is defined between flux density and frequency through S ∝ ν−α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' In the Healpy pixelation scheme, the sky is divided into equal area pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For a given pixel p with Np sources having spectral indices αi,p, we 3These estimates correspond to NVSS galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Assuming the NVSS measured dipole in LSS is true, we expect similar numbers from SKA continuum surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 4https://healpy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='io/en/latest/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content='html Page 8 of J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Astr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' (0000) 000: define mean spectral index ¯αp = 1 Np � i αi,p (11) here i runs over all the sources in pixel p Exponent (x) of differential number count – De- fined using N(S, ˆn) ∝ S −1−x Average Flux Density ( ¯S ) – We define this quan- tity for a pixel p ¯S p = 1 Np � i S i,p (12) where again i runs over all the sources in p and Np is the number of sources in the pixel The spectral index characterises the morphology of an astronomical source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Angular dependence of ¯α has not been much looked at in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Analysing the dipole anisotropy in ¯α has been a challenge since it requires reliable multi-frequency continuum radio sky survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Such an SKA survey can be used to estimate this anisotropy if the flux density of the sources at dif- ferent frequencies is measured with sufficient accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' For x, the angular dependency was analysed by (Ghosh & Jain, 2017) in NVSS data using likelihood maximisa- tion and the results were found to be consistent with CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' However, with a larger expected source count of SKA that is almost twice in comparison to NVSS, angular dependence analysis of x may provide a more stringent test of CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' SKA will also be able to test the phenomenon of alignment of radio galaxy axes and integrated polariza- tions, as claimed in earlier radio observations (Tiwari & Jain, 2013, 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Taylor & Jagannathan, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Conclusion and Outlook In this paper, we have reviewed several cosmological signals which appear to show a violation of CP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We have also reviewed a model, based on aligned super- horizon modes which can explain some of these obser- vations along with the Hubble tension (Tiwari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The model can be theoretically justified by pos- tulating a pre-inflationary phase during which the Uni- verse may not be homogeneous and isotropic (Rath et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' The model leads to several cosmolog- ical predictions which can be tested at SKA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' By us- ing the best fit parameters with current observations, we have determined the redshift dependence of the pre- dicted dipole in radio galaxy number counts and associ- ated uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' As can be seen from Figure 2, SKA can test this very reliably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' If this prediction is confirmed by SKA, it may provide us with a first glimpse into the Physics of the pre-inflationary phase of the Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We have also suggested other isotropy tests with SKA using other variables which are independent of number density and thus are more robust under unequal coverage and systematics of the sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' These variables are (a) mean spectral index ¯α, (b) exponent of the dif- ferential number count x & (c) average flux density ¯S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' Acknowledgements RK is supported by the South African Radio Astron- omy Observatory and the National Research Founda- tion (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 75415).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' PT acknowledges the support of the RFIS grant (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 12150410322) by the National Natural Science Foundation of China (NSFC) and the support by the National Key Basic Research and De- velopment Program of China (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' 2018YFA0404503) and NSFC Grants 11925303 and 11720101004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' SG is supported in part by the National Key R & D Pro- gram of China (2021YFC2203100), by the Fundamen- tal Research Funds for the Central Universities under grant no: WK2030000036, and the NSFC grant no: 11903030.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' We are also very thankful to the anonymous referee whose comments were really helpful in improv- ing the presentation of the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=' References Alonso, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', Bull, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/3tE1T4oBgHgl3EQfSQPo/content/2301.03065v1.pdf'} +page_content=', Ferreira, P.' metadata={'source': 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