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is lighter than the gravitino by an amount determined by the slow roll parameter . The existence of slow-roll conditions
is directly linked to the values of supersymmetry and R-symmetry breaking scales. We make cosmological predictions
of our model and compare them to current data.
Key words: SUSY; cosmology; in
ation
1. Introduction
In spite of the enormous success of in
ationary cosmol-
ogy [1, 2, 3, 4, 5, 6, 7, 8, 9] at describing the observed
properties of the Universe, we are still missing a deriva-
tion from rst principles where the in
aton eld is iden-
ti ed with one, or several, fundamental elds in particle
physics. This manifests itself the in the fact that we still
do not count with a natural way of identifying the in
aton
eld and the properties of its potential required to satisfy
experimental constraints [10, 11].
It was quickly realized after the in
ationary scenario
was proposed more than 30 years ago, that supersymmetry
could provide a natural scenario with plenty of
at direc-
tions which could lead to in
ation [18, 19, 20, 21, 22, 23].
When the theory couples to supergravity, there are a num-
Email addresses: Luis.Alvarez-Gaume@cern.ch (Luis
Alvarez-Gaum e), cesar.gomez@uam.es (C esar G omez),
jimenez@icc.ub.edu (Raul Jimenez)ber of new problems that appear [24], and we will discuss
some of them later on.
Current observational constraints from CMB tempera-
ture and polarization experiments and large-scale struc-
ture limit the amount the in
aton eld has moved to ap-
proximately <2Mpl[14], where Mplis the reduced Planck
mass. Therefore, in
ationary models that search for the
in
aton at very large energies, like for example chaotic
in
ation, are severely constrained already by current ob-
servations. With the current new generation of CMB ex-
periments (Planck, EBEX, Spider, SPUDS etc...) it will
be possible to further constraint how much the in
aton
eld has displaced during the in
ationary period that gave
rise to our current casual horizon. It is therefore useful to
revisit again the problem of steep directions in SUGRA
models to understand if a
at direction can be obtained at
all.
In this paper we will suggest a natural embedding of in-
ationary dynamics in the e ective low-energy Lagrangian
Preprint submitted to Physics Letters B October 26, 2018arXiv:1001.0010v1 [hep-th] 30 Dec 2009describing supersymmetry breaking. Our approach will
be quite independent of the microphysics underlying su-
persymmetry breaking, and will only rely on universal
properties of this symmetry. Since we are not commit-
ting ourselves to any particular microscopic realization of
supersymmetry breaking, some of our comments about re-
heating for instance will be rather sketchy. A more de-
tailed and precise presentations of our ideas will appear
elsewhere [25]. Like most in
ationary theories containing
supersymmetry, we present a simple model of multi eld
in
ation (sometimes called hybrid) [26], identify naturally
the in
aton eld and its potential, and then t a few obser-
vational data to estimate the few parameters of our model.
We compute, in particular, the number of e-folding and the
amplitude of density
uctuations at horizon crossing. It is
surprising to nd that the scale of supersymmetry break-
ing indicated by this analysis is between 10111014GeV.
An interesting spin-o of our model is that the in
aton is
lighter than the gravitino by an amountp, whereis
one of the slow roll parameters (see below).
We would like to stress that in this paper we are always
assuming F-breaking of supersymmetry. In D-breaking
scenarios our arguments do not apply, at least as presented
here1.
2. General framework
Supersymmetry is a natural framework to de ne in-
ationary scenarios for two main reasons. First of all,
SUSY naturally leads to the existence of
at, or nearly
at directions (pseudomoduli), allowing for slow roll sce-
narios. Second, and more important, the order parameter
of supersymmetry breaking is the vacuum energy density.
Hence, naturally associated with its breaking, supersym-
metry contains two main ingredients necessary in in
a-
tionary scenarios: vacuum energy and reasonably
at di-
rections.