diff --git "a/8tE0T4oBgHgl3EQffgDC/content/tmp_files/load_file.txt" "b/8tE0T4oBgHgl3EQffgDC/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/8tE0T4oBgHgl3EQffgDC/content/tmp_files/load_file.txt" @@ -0,0 +1,1080 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf,len=1079 +page_content='Prepared for submission to JCAP Constraining primordial non-Gaussianity by combining next-generation galaxy and 21 cm intensity mapping surveys Sheean Jolicoeur1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Roy Maartens1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Simthembile Dlamini1 1Department of Physics & Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' University of the Western Cape,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Cape Town 7535,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' South Africa 2Institute of Cosmology & Gravitation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' University of Portsmouth,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Portsmouth PO1 3FX,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' United Kingdom 3National Institute for Theoretical & Computational Sciences (NITheCS),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Cape Town 7535,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' South Africa Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Surveys of the matter distribution contain ‘fossil’ information on possible non- Gaussianity that is generated in the primordial Universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' This primordial signal survives only on the largest scales where cosmic variance is strongest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' By combining different surveys in a multi-tracer approach, we can suppress the cosmic variance and significantly improve the precision on the level of primordial non-Gaussianity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We consider a combination of an optical galaxy survey, like the recently initiated DESI survey, together with a new and very different type of survey, a 21 cm intensity mapping survey, like the upcoming SKAO survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' A Fisher forecast of the precision on the local primordial non-Gaussianity parameter fNL, shows that this multi-tracer combination, together with non-overlap single-tracer information, can deliver precision comparable to that from the CMB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Taking account of the largest systematic, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' foreground contamination in intensity mapping, we find that σ(fNL) ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='02406v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='CO] 6 Jan 2023 Contents 1 Introduction 1 2 Multi-tracer power spectra 2 3 Modelling the surveys 3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='1 Noise 5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2 Intensity mapping beam and foregrounds 6 4 Fisher forecast 7 5 Conclusion 9 1 Introduction Constraining the local primordial non-Gaussianity (PNG) parameter fNL presents an impor- tant challenge for next-generation large-scale structure surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Local-type PNG affects the power spectrum of dark matter tracers by inducing a scale-dependent correction to the tracer bias [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' This correction is strongly suppressed on small to medium scales, but on very large scales, it is ∝ fNL(H2 0/k2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' This means that ultra-large survey volumes are required for high-precision constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The Planck survey of the cosmic microwave background (CMB) gives the current state- of-the-art constraint σ(fNL) = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='1 from the bispectrum [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Future CMB surveys will lead to an improvement on the Planck precision, but not by much and not sufficient to access σ(fNL) ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' This level of precision would enable us to rule out many single-field and multi- field inflationary scenarios [4–6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The hope is that this goal can be achieved by using the extra modes in 3-dimensional surveys of the large-scale structure (see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' [7–12]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' However, extracting fNL from these surveys faces formidable difficulties: Observational systematics on very large scales [13–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For our simplified Fisher anal- ysis, we neglect these systematics, except for the foreground contamination of 21 cm intensity mapping (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Astrophysical complications entailed in the modelling of tracer clustering, in particular, the uncertainties in modelling the scale-dependent bias [20, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We use a simplified model since a full treatment requires simulations, beyond the scope of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' A theoretical systematic arising from the neglect of lensing magnification and other relativistic lightcone effects on the power spectrum, which can bias the best-fit fNL [22–35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Although the bias on best-fit can be large, the error σ(fNL) is not significantly affected and we therefore omit these lightcone effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Cosmic (or sample) variance that dominates ultra-large scale measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We deal with this problem via a multi-tracer approach – which also helps to mitigate uncorrelated systematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' – 1 – Recent constraints on fNL have used the BOSS galaxy [36] and eBOSS quasar [37] samples, with the tightest constraint to date of σ(fNL) = 21 from eBOSS [38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The much larger volumes of upcoming surveys should facilitate significant improvement on this precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' But if we rely on individual surveys using the power spectrum of single tracers, it turns out that σ(fNL) ≲ 1 is not achievable – even if we neglect systematics and complexities in scale- dependent bias [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The fundamental problem is cosmic variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' A way to evade cosmic variance is the multi-tracer technique [39–48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Forecasts indicate that multi-tracing next-generation surveys can surpass the CMB precision, and in some cases can achieve σ(fNL) ≲ 1 [47–60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The performance of the multi-tracer improves when the difference in tracer properties, especially the Gaussian clustering biases, is significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' It also helps to suppress uncorrelated systematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' In this paper, our aim is not to identify survey combinations that can achieve σ(fNL) ≲ 1 – for this purpose, one typically requires the very high number densities of photometric sur- veys [47, 51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Instead, our aim is to investigate the improvements over single-tracer constraints when using a new type of spectroscopic large-scale structure survey – neutral hydrogen (HI) intensity mapping of the 21 cm emission line – in combination with spectroscopic galaxy sur- veys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Such a pair of spectroscopic samples has very different clustering biases and systematics, which accentuates the advantages of a multi-tracer analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We use a simple Fisher forecast on mock surveys, which are based on next-generation surveys that are starting to observe or close to starting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The two surveys we have in mind are: the Dark Energy Spectroscopic Instrument (DESI), with the Bright Galaxy Sample (BGS) and Emission Line Galaxy (ELG) samples [61, 62], and the Square Kilometre Array Observatory (SKAO), with intensity mapping surveys in Bands 1 and 2 [56, 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Galaxy number count surveys are well established, but a cosmological HI intensity mapping survey has not yet been implemented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' However, pilot surveys on the SKAO precursor telescope MeerKAT have already been used to: (a) measure the cross-power between MeerKAT and WiggleZ galaxy surveys [64], and (b) start developing a pipeline for the planned SKAO surveys [65, 66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We combine pairs of these surveys at low and high redshifts, using the Fisher single- tracer constraints in the non-overlap volume and the multi-tracer constraints in the overlap volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The results show a reasonable improvement for the low-redshift pair, and a significant improvement for the high-redshift pair, compared to the standard single-tracer forecasts for σ(fNL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The combination of all low- and high-redshift surveys improve on Planck, with σ(fNL) ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' This constraint is based on avoiding foreground contamination of HI intensity mapping on very large scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Foreground contamination of HI intensity mapping has a strong effect on the precision: if we neglect this foreground contamination, we find that σ(fNL) ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 2 Multi-tracer power spectra At first order in perturbations, the density (or temperature) contrast of a tracer A is related to the matter density contrast δ by ∆A(z, k) = � bA(z) + f(z)µ2� δ(z, k) , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='1) where bA is the (Gaussian) clustering bias, µ = ˆk · n is the projection along the line-of-sight direction n, and f is the linear growth rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We assume bA has a known redshift evolution βA, following [67], so that bA(z) = bA0 βA(z) , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2) – 2 – where the amplitude bA0 is a free parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We highlight the point that a multi-tracer approach reduces the impact of this assumption on σ(fNL) [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The Fourier power spectra at tree-level are given by � ∆A(z, k)∆B(z, k′) � = (2π)3PAB(z, k)δD(k + k′) , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3) where the linear matter power spectrum (computed using CLASS [68]) is PAB = � bA + fµ2�� bB + fµ2� P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='4) In the presence of local PNG, the bias acquires a scale-dependent correction: ˆbA(z, k) = bA(z) + bAφ(z) fNL M(z, k) , M(z, k) = 2 3Ωm0H2 0 D(z) gin T(k) k2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='5) Here T(k) is the matter transfer function (normalized to 1 on very large scales), D is the growth factor (normalized to 1 today) and gin is the initial growth suppression function, defined deep in the matter era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For ΛCDM gin = 3 5 � 1 + z � D � 1 + 2f 3Ωm � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='6) The non-Gaussian bias factor bAφ is halo-dependent and should be determined with the aid of simulations [20, 69, 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' A simplified model reduces it to bAφ(z) = 2δc � bA(z) − pA � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='7) where the critical collapse density is given by δc = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='686 and pA are halo-dependent constants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' In the simplest (universal) halo model, pA = 1 for all tracers A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' But this model is not consistent with simulations [20, 69, 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' An improved (but still over-simplified) model allows the constant pA to vary with tracer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For galaxies chosen by stellar mass, simulations indicate that the rough approximation [69] pg ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='55 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8) is an improvement, and we use this for the DESI-like samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For HI intensity mapping, we use the approximation [70] pH ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='25 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='9) The fNL terms in the power spectra are of order H2 0/k2 on ultra-large scales, k ≲ keq, where T ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Local PNG therefore dominates the power on ultra-large scales – but these are also the scales where cosmic variance is largest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We deal with the cosmic variance via a multi-tracer analysis, which includes the information from all auto- and cross-power spectra of the two (or more) tracers (see section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 3 Modelling the surveys We consider two mock spectroscopic surveys: A = g: galaxy survey, similar to DESI surveys [61, 62];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' A = H: 21 cm HI intensity mapping (IM) survey, similar to SKAO surveys [56, 63, 71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' In both cases, we have a low- and a high-redshift survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The sky and redshift coverage of the individual and overlapping surveys are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' – 3 – Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Sky area and redshift range of surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Survey Sample Ωsky ttot redshift � 103 deg2� � 103 hr � range g (DESI-like) BGS 14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='00–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='50 ELG 14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='60–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='70 H (SKAO-like) Band 2 20 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='10–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='58 Band 1 20 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='35–3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='05 g × H (low z) BGS × Band 2 10 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='10–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='50 g × H (high z) ELG × Band 1 10 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='60–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='70 0 1 2 3 z 10−4 10−3 10−2 ng [ h3 Mpc 3] BGS ELG HI 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='5 ¯TH [ mK] Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Background comoving galaxy number densities (red, left-hand y-axis) and HI IM temper- ature (blue, right-hand y-axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The one-parameter model (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2) for the Gaussian clustering bias of the galaxy surveys follows [29] bg(z) = bg0 D(z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='1) Fiducial values are bg0 = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='34 for the Bright Galaxy Sample (BGS) and bg0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='84 for the Emission Line Galaxy (ELG) sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For the HI IM surveys we use a fit based on [72, 73]: bH(z) = bH0 � 1 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='823 z − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='0546 z2� with fiducial value bH0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='842 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2) The background comoving number density ¯ng for the BGS and ELG samples is modelled fol- lowing [29], which leads to the smoothed curves shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For HI IM, the background brightness temperature is modelled via the fit given in [65, 74]: ¯TH(z) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='0559 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2324 z − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='0241 z2 mK , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3) which is also shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' – 4 – 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='1 Noise In galaxy surveys, the shot noise (assumed to be Poissonian) is P shot gg (z) = 1 ¯ng(z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='4) Then the total signal that we measure for the galaxy auto-power spectrum is ˜Pgg(z, k, µ) = Pgg(z, k, µ) + P shot gg (z) , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='5) where Pgg is given by (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' In IM surveys, there is shot noise, but also thermal (or instrumental) noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The Poisso- nian shot noise (see [75] for non-Poissonian corrections) is derived in a halo-model framework and given by [72, 76], P shot HH (z) = 1 ¯nH(z) = 1 ¯ρ 2 H(z) � dM Nh(M, z) M2 H(M, z) , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='6) where ¯nH is the effective average comoving number density of HI, ¯ρH is the average comoving HI density, Nh is the halo mass function (average comoving halo number density per mass) and MH is the average HI mass in a halo of mass M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' However, on the linear scales that we consider, the shot noise is much smaller than the thermal noise and can be safely neglected [72, 76].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The thermal noise in HI IM depends on the sky temperature in the radio band, the survey specifications and the array configuration (single-dish or interferometer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For the single-dish mode of SKAO-like surveys, the thermal noise power spectrum is [77–79]: P therm HH (z) = Ωsky 2ν21ttot (1 + z)r(z)2 H(z) �Tsys(z) ¯TH(z) �2 1 Nd , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='7) where ν21 = 1420 MHz is the rest-frame frequency of the 21 cm emission, ttot is the total observing time, and the number of dishes is Nd = 197 (with dish diameter Dd = 15 m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The system temperature is modelled as [80]: Tsys(z) = Td(z) + Tsky(z) = Td(z) + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='7 + 25 �400 MHz ν21 (1 + z) �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='75 K, (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8) where Td is the dish receiver temperature (see [71]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The total signal is then ˜PHH(z, k, µ) = PHH(z, k, µ) + P shot HH (z) + P therm HH (z) ≈ PHH(z, k, µ) + P therm HH (z) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='9) The noise for all surveys is shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' In the case of the cross-power spectrum PgH, cross-shot noise arises if the halos that host galaxies and HI overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Following the arguments given in [71, 81], we assume that the cross-shot noise may be neglected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The total cross-power signal is then ˜PgH = PgH with P shot gH ≈ 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='10) – 5 – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='5 z 102 103 104 P shot gg [h−3 Mpc3] BGS ELG 1 2 3 z 101 102 103 P therm HH [h−3 Mpc3] Band 2 Band 1 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Shot noise for galaxy surveys (left) and thermal noise for IM surveys (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2 Intensity mapping beam and foregrounds HI IM surveys like the SKAO surveys have poor angular resolution, which results in power loss on small transverse scales, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' for large k⊥ = (1 − µ2)1/2k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' This effect is typically modelled by a Gaussian beam factor [77]: Db(z, k, µ) = exp � −(1 − µ2)k2r(z)2θb(z)2 16 ln 2 � with θb(z) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='22 λ21(1 + z) Dd .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='11) HI IM surveys are also contaminated by foregrounds that are much larger than the HI signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Since these foregrounds are spectrally smooth, they can be separated from the non- smooth signal on small to medium scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' However, on very large radial scales, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' for small k∥ = µk, the signal becomes smoother and therefore the separation fails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' A comprehensive treatment includes simulations of foreground cleaning of the HI signal (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' [15, 18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For a simplified Fisher forecast we can instead use a foreground avoidance approach, by excising the regions of Fourier space where the foregrounds are significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' This means removing large radial scales, which can be modelled via an exponential suppression factor [73, 82]: Dfg(k, µ) = 1 − exp � − �µk kfg �2� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='12) We choose a typically used value: kfg = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='01 h Mpc−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='13) Figure 3 illustrates the consequences of foreground avoidance for the monopoles of the HI power spectra, PAH,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' It is clear that large-scale (small k) power in PAH,0 is lost and that the effect of local PNG on these large scales is suppressed by foreground avoidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Note that fNL reduces the HI power on very large scales at z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3, since bH < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='25, which leads to bHφ < 0 in (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Also note that the beam effect on PAH,0, which tends to suppress small scale (large k) modes, is negligible at the low redshift, but becomes apparent at higher redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' In summary, the effects of the radio telescope beam and radio foreground avoidance lead to the following modifications of the power spectra PAH: PHH(z, k, µ) → Dfg(k, µ) Db(z, k, µ)2 PHH(z, k, µ) , (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='14) PgH(z, k, µ) → Dfg(k, µ) Db(z, k, µ) PgH(z, k, µ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='15) – 6 – 10−3 10−2 10−1 k [h Mpc−1] 101 102 103 104 PAB, 0 [h−3 Mpc3] k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='01 BGS Band 2 BGS × Band 2 fNL = 0 fNL = 10 10−3 10−2 10−1 k [h Mpc−1] 101 102 103 104 PAB, 0 [h−3 Mpc3] k = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='01 ELG Band 1 ELG × Band 1 fNL = 0 fNL = 10 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The monopole power spectra at z = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3 (left) and z = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='0 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 4 Fisher forecast For a multi-tracer combination of two dark matter tracers g and H, the data vector of power spectra is P = � Pgg , PgH , PHH � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='1) We exclude the noise from the data vector, since the noise is independent of the cosmolog- ical and nuisance parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (The noise appears in the covariance, as given below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=') The standard cosmological parameters are measured on medium to small scales and are effectively independent of the ultra-large scale parameter fNL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Fixing their values could bias the best-fit value of fNL but is unlikely to have any significant impact on σ(fNL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We include in the Fisher analysis the cosmological parameters that directly affect the large-scale amplitude (σ8,0) and shape (ns) of the power spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We therefore consider the following cosmological and nuisance parameters: ϑα = � σ8,0, ns, fNL;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' bg0, bH0 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2) Here we assume that the degeneracies between bA and σ8,0, and between ¯TH and σ8,0, have been broken by other surveys that focus on medium to small scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The covariance for the multi-tracer power spectra is given by [83, 84]: Cov(P , P ) = k3 f 4πk2∆k 2 ∆µ � � � � � � � ˜P 2 gg ˜Pgg ˜PgH ˜P 2 gH ˜Pgg ˜PgH 1 2 � ˜Pgg ˜PHH + ˜P 2 gH � ˜PHH ˜PgH ˜P 2 gH ˜PHH ˜PgH ˜P 2 HH � � � � � � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3) Here ∆k and ∆µ are the bin-widths for k and µ and kf is the fundamental mode, corresponding to the longest wavelength, which is determined by the comoving survey volume of the redshift bin centred at z: V (z) = Ωsky 3 � r � z + ∆z 2 �3 − r � z − ∆z 2 �3� = � 2π kf(z) �3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='4) – 7 – Then the multi-tracer Fisher matrix in a redshift bin is F P αβ = +1 � µ=−1 kmax � k=kmin ∂α P · Cov(P , P )−1 · ∂β P T , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='5) where ∂α = ∂ / ∂ϑα.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We choose the bin-widths and kmin following [85–87]: ∆µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='04 , ∆k = kf , kmin = kf .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='6) The smallest scale (largest k) is chosen to ensure that linear perturbations remain accurate, since we do not require information from nonlinear scales: kmax = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='08(1 + z)2/(2+ns) h Mpc−1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='7) The galaxy and HI IM surveys do not have the same sky area and redshift ranges (see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The overlap redshift ranges are obvious;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' for the sky areas, we assume a nominal overlap area of 10,000 deg2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The multi-tracer applies in the overlap redshift range and overlap sky area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' However, we can add the independent Fisher matrices obtained in the non-overlapping regions of the two individual surveys to the multi-tracer Fisher matrix in the overlapping region [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' In detail, the non-overlap region is the non-overlap sky area of each survey, across the full redshift range of each survey;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' the overlap sky area, across the non-overlap parts of the redshift ranges of each survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Then the full Fisher matrix (denoted by g ⊗ H) is F g⊗H αβ = F P αβ(overlap) + F g αβ(non-overlap) + F H αβ(non-overlap).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8) Figure 4 shows the 1σ error contours computed from this Fisher matrix after marginalising over the bias parameters in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We use the fiducial values σ8,0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8102, ns = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='9665 and fNL = 0, keeping other cosmological parameters fixed to their Planck 2018 best-fit values [88].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Table 2 lists the marginalised σ(fNL) constraints, including the improvements (in parentheses) that follow when we ignore the HI IM foregrounds, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' when kfg = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' – 8 – 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='83 σ8, 0 −40 0 40 fNL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='96 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='98 ns σ8, 0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8102 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='96 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='98 ns ns = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='9665 −20 20 fNL fNL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='0 BGS Band 2 BGS ⊗ Band 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='806 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='814 σ8, 0 −5 0 5 fNL 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='962 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='966 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='970 ns σ8, 0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8102 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='963 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='970 ns ns = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='9665 −5 0 5 fNL fNL = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='0 ELG Band 1 ELG ⊗ Band 1 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 1σ contours, including foreground avoidance in HI intensity mapping and marginalising over bias parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Cumulative marginalised error σ(fNL) for: the single-tracer surveys;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' the low-z and high-z multi-tracer pairs – including single-tracer information from the non-overlap volumes as in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' and the sum of the multi-tracer pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Values in parenthesis correspond to ignoring foregrounds, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=', with kfg = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Survey σ(fNL) BGS 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8 ELG 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='5 Band 2 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3 (57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='7) Band 1 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3) BGS ⊗ Band 2 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3) ELG ⊗ Band 1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='2 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3) BGS ⊗ Band 2 + ELG ⊗ Band 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='9 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='1) 5 Conclusion We applied a simplified Fisher forecast analysis in order to gain insights into the improvements on σ(fNL) from a new multi-tracer combination of large-scale structure surveys that will be made possible by the upcoming HI intensity mapping surveys with the SKAO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For the spectroscopic galaxy samples, we used mock surveys based on DESI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' This allowed for multi- tracer pairs at low and high redshifts, in order to see the level of improved precision from the higher volume at high redshifts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We included all available Fisher information from these mock surveys, using the multi- tracer Fisher matrix on the overlap volume (sky area and redshift range) and the single-tracer Fisher matrices on the non-overlap volumes, as in (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Our results for σ(fNL) are summarised – 9 – in Table 2, which gives the single-tracer results for the 4 samples, the full multi-tracer results from (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='8) for the low- and high-redshift pairs, and finally the results from the Fisher sum of these pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The impact of foreground avoidance can be seen from the results (in parenthesis) when foregrounds are ignored, corresponding to kfg = 0 in (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Figure 4 shows the 1σ contours for the 3 cosmological parameters (σ8, 0, ns, fNL), marginalising over the 2 bias nuisance parameters (bg0, bH0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' As expected, the foreground avoidance severely degrades the constraining power of the HI intensity surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Without foregrounds, the high-redshift Band 1 survey would perform as well as the multi-tracer combination with the ELG survey: σ(fNL) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The reduced precision on fNL for single-tracer HI intensity constraints is consistent with the findings of [15], where foreground cleaning is simulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' However, using the multi-tracer with a spectroscopic galaxy survey helps to reduce the effect of foregrounds on σ(fNL), as shown by Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' The multi-tracer analysis is also expected to mitigate other systematics in the galaxy and HI intensity samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' For example, HI intensity mapping is also affected by radio frequency interference, receiver noise, calibration errors and polarisation leakage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Incorporating these and the galaxy systematics requires extensive simulations, beyond the scope of our paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' – 10 – Acknowledgements We thank Dionysis Karagiannis for very helpful comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' We are supported by the South African Radio Astronomy Observatory (SARAO) and the National Research Foundation (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 75415).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' References [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Matarrese and L.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='nnnnn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' [85] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Karagiannis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Lazanu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Liguori, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Raccanelli, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Bartolo, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Verde, Constraining primordial non-Gaussianity with bispectrum and power spectrum from upcoming optical and radio surveys, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 478 (2018), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 1 1341–1376, [arXiv:1801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='09280].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' [86] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Yankelevich and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Porciani, Cosmological information in the redshift-space bispectrum, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Roy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 483 (2019), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 2 2078–2099, [arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='07076].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' [87] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Maartens, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Jolicoeur, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Umeh, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' De Weerd, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Clarkson, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Camera, Detecting the relativistic galaxy bispectrum, JCAP 03 (2020), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 03 065, [arXiv:1911.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='02398].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' [88] Planck Collaboration, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Aghanim et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=', Planck 2018 results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Cosmological parameters, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 641 (2020) A6, [arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='06209].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' [Erratum: Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content='Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' 652, C4 (2021)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'} +page_content=' – 15 –' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8tE0T4oBgHgl3EQffgDC/content/2301.02406v1.pdf'}