10,381 research outputs found
Inflation and Reheating in Spontaneously Generated Gravity
Inflation is studied in the context of induced gravity (IG) , where is the Ricci scalar, a scalar field and a
dimensionless constant, and diverse symmetry-breaking potentials
are considered. In particular we compared the predictions for Landau-Ginzburg
(LG) and Coleman-Weinberg (CW) type potentials and their possible
generalizations with the most recent data. We find that large field inflation
generally leads to fewer constraints on the parameters and the shape of the
potential whereas small field inflation is more problematic and, if viable,
implies more constraints, in particular on the parameter . We also
examined the reheating phase and obtained an accurate analytical solution for
the dynamics of inflaton and the Hubble parameter by using a multiple scale
analysis (MSA). The solutions were then used to study the average expansion of
the Universe, the average equation of state for the scalar field and both the
perturbative and resonant decays of the inflaton field.Comment: 15 pages, 10 figures, to be published in Phys. Rev.
Reconstruction of Scalar Potentials in Modified Gravity Models
We employ the superpotential technique for the reconstruction of cosmological
models with a non-minimally coupled scalar field evolving on a spatially flat
Friedmann-Robertson-Walker background. The key point in this method is that the
Hubble parameter is considered as a function of the scalar field and this
allows one to reconstruct the scalar field potential and determine the dynamics
of the field itself, without a priori fixing the Hubble parameter as a function
of time or of the scale factor. The scalar field potentials that lead to de
Sitter or asymptotic de Sitter solutions, and those that reproduce the
cosmological evolution given by Einstein-Hilbert action plus a barotropic
perfect fluid, have been obtained.Comment: 12 pages, 2 figures, accepted for publication in PR
Stochastic growth of quantum fluctuations during slow-roll inflation
We compute the growth of the mean square of quantum fluctuations of test
fields with small effective mass during a slowly changing, nearly de Sitter
stage which took place in different inflationary models. We consider a
minimally coupled scalar with a small mass, a modulus with an effective mass (with as the Hubble parameter) and a massless non-minimally
coupled scalar in the test field approximation and compare the growth of their
relative mean square with the one of gauge-invariant inflaton fluctuations. We
find that in most of the single field inflationary models the mean square gauge
invariant inflaton fluctuation grows {\em faster} than any test field with a
non-negative effective mass. Hybrid inflationary models can be an exception:
the mean square of a test field can dominate over the gauge invariant inflaton
fluctuation one on suitably choosing parameters. We also compute the stochastic
growth of quantum fluctuation of a second field, relaxing the assumption of its
zero homogeneous value, in a generic inflationary model; as a main result, we
obtain that the equation of motion of a gauge invariant variable associated,
order by order, with a generic quantum scalar fluctuation during inflation can
be obtained only if we use the number of e-folds as the time variable in the
corresponding Langevin and Fokker-Planck equations for the stochastic approach.
We employ this approach to derive some bounds in the case of a model with two
massive fields.Comment: 9 pages, 4 figures. Added references, minor changes, matches the
version to be published in Phys. Rev.
Interdependence between integrable cosmological models with minimal and non-minimal coupling
We consider the relation between exact solutions of cosmological models
having minimally and non-minimally coupled scalar fields. This is done for a
particular class of solvable models which, in the Einstein frame, have
potentials depending on hyperbolic functions and in the Jordan frame, where the
non-minimal coupling is conformal, possess a relatively simple dynamics. We
show that a particular model in this class can be generalized to the cases of
closed and open Friedmann universes and still exhibits a simple dynamics.
Further we illustrate the conditions for the existences of bounces in some
sub-classes of the set of integrable models we have considered.Comment: 15 pages, v2: figures and references added, accepted for publication
in CQ
Integrable cosmological models with non-minimally coupled scalar fields
We obtain general solutions for some flat Friedmann universes filled with a
scalar field in induced gravity models and models including the
Hilbert-Einstein curvature term plus a scalar field conformally coupled to
gravity. As is well known, these models are connected to minimally coupled
models through the combination of a conformal transformation and a
transformation of the scalar field. The explicit forms of the self-interaction
potentials for six exactly solvable models are presented here. We obtain the
general solution for one of the integrable models, namely, the induced gravity
model with a power-law potential for the self-interaction of the scalar field.
We argue that although being mathematically in a one-to-one correspondence with
the solutions in the minimally coupled models, the solutions in the
corresponding non-minimally coupled models are physically different. This is
because the cosmological evolutions seen by an internal observer connected with
the cosmic time can be quite different. The study of a few induced gravity
models with particular potentials gives us an explicit example of such a
difference.Comment: 20 pages, v3: references added, accepted for publication in CQ
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