17 research outputs found
The evolution of density perturbations in f(R) gravity
We give a rigorous and mathematically well defined presentation of the
Covariant and Gauge Invariant theory of scalar perturbations of a
Friedmann-Lemaitre-Robertson-Walker universe for Fourth Order Gravity, where
the matter is described by a perfect fluid with a barotropic equation of state.
The general perturbations equations are applied to a simple background solution
of R^n gravity. We obtain exact solutions of the perturbations equations for
scales much bigger than the Hubble radius. These solutions have a number of
interesting features. In particular, we find that for all values of n there is
always a growing mode for the density contrast, even if the universe undergoes
an accelerated expansion. Such a behaviour does not occur in standard General
Relativity, where as soon as Dark Energy dominates, the density contrast
experiences an unrelenting decay. This peculiarity is sufficiently novel to
warrant further investigation on fourth order gravity models.Comment: 21 pages, 2 figures, typos corrected, submitted to PR
Cosmological dynamics of exponential gravity
We present a detailed investigation of the cosmological dynamics based on
gravity. We apply the dynamical system approach to both
the vacuum and matter cases and obtain exact solutions and their stability in
the finite and asymptotic regimes. The results show that cosmic histories exist
which admit a double de-Sitter phase which could be useful for describing the
early and the late-time accelerating universe.Comment: 17 pages LaTeX, 3 figure
Compactifying the state space for alternative theories of gravity
In this paper we address important issues surrounding the choice of variables
when performing a dynamical systems analysis of alternative theories of
gravity. We discuss the advantages and disadvantages of compactifying the state
space, and illustrate this using two examples. We first show how to define a
compact state space for the class of LRS Bianchi type I models in -gravity
and compare to a non--compact expansion--normalised approach. In the second
example we consider the flat Friedmann matter subspace of the previous example,
and compare the compact analysis to studies where non-compact
non--expansion--normalised variables were used. In both examples we comment on
the existence of bouncing or recollapsing orbits as well as the existence of
static models.Comment: 18 pages, revised to match published versio
Dynamics of f(R)-cosmologies containing Einstein static models
We study the dynamics of homogeneous isotropic FRW cosmologies with positive
spatial curvature in -gravity, paying special attention to the existence
of Einstein static models and only study forms of for which these
static models have been shown to exist. We construct a compact state space and
identify past and future attractors of the system and recover a previously
discovered future attractor corresponding to an expanding accelerating model.
We also discuss the existence of universes which have both a past and future
bounce, a phenomenon which is absent in General Relativity.Comment: 14 pages, 6 figure
Cosmological dynamics of R^n gravity
A detailed analysis of dynamics of cosmological models based on
gravity is presented. We show that the cosmological equations can be written as
a first order autonomous system and analyzed using the standard techniques of
dynamical system theory. In absence of perfect fluid matter, we find exact
solutions whose behavior and stability are analyzed in terms of the values of
the parameter . When matter is introduced, the nature of the (non-minimal)
coupling between matter and higher order gravity induces restrictions on the
allowed values of . Selecting such intervals of values and following the
same procedure used in the vacuum case, we present exact solutions and analyze
their stability for a generic value of the parameter . From this analysis
emerges the result that for a large set of initial conditions an accelerated
expansion is an attractor for the evolution of the cosmology. When matter
is present a transient almost-Friedman phase can also be present before the
transition to an accelerated expansion.Comment: revised and extended version, 35 pages, 12 tables, 14 figures which
are not included and can be found at http://www.mth.uct.ac.za/~peter/R
f(R) Gravity with Torsion: The Metric-Affine Approach
The role of torsion in f(R) gravity is considered in the framework of
metric-affine formalism. We discuss the field equations in empty space and in
presence of perfect fluid matter taking into account the analogy with the
Palatini formalism. As a result, the extra curvature and torsion degrees of
freedom can be dealt as an effective scalar field of fully geometric origin.
From a cosmological point of view, such a geometric description could account
for the whole Dark Side of the Universe.Comment: 12 page
Torsion and accelerating expansion of the universe in quadratic gravitation
Several exact cosmological solutions of a metric-affine theory of gravity
with two torsion functions are presented. These solutions give a essentially
different explanation from the one in most of previous works to the cause of
the accelerating cosmological expansion and the origin of the torsion of the
spacetime. These solutions can be divided into two classes. The solutions in
the first class define the critical points of a dynamical system representing
an asymptotically stable de Sitter spacetime. The solutions in the second class
have exact analytic expressions which have never been found in the literature.
The acceleration equation of the universe in general relativity is only a
special case of them. These solutions indicate that even in vacuum the
spacetime can be endowed with torsion, which means that the torsion of the
spacetime has an intrinsic nature and a geometric origin. In these solutions
the acceleration of the cosmological expansion is due to either the scalar
torsion or the pseudoscalar torsion function. Neither a cosmological constant
nor dark energy is needed. It is the torsion of the spacetime that causes the
accelerating expansion of the universe in vacuum. All the effects of the
inflation, the acceleration and the phase transformation from deceleration to
acceleration can be explained by these solutions. Furthermore, the energy and
pressure of the matter without spin can produce the torsion of the spacetime
and make the expansion of the universe decelerate as well as accelerate.Comment: 20 pages. arXiv admin note: text overlap with gr-qc/0604006,
arXiv:1110.344
Some remarks on the dynamical systems approach to fourth order gravity
Building on earlier work, we discuss a general framework for exploring the
cosmological dynamics of Higher Order Theories of Gravity. We show that once
the theory of gravity has been specified, the cosmological equations can be
written as a first-order autonomous system and we give several examples which
illustrate the utility of our method. We also discuss a number of results which
have appeared recently in the literature.Comment: 19 pages, LaTe
Spherical symmetry in -gravity
Spherical symmetry in gravity is discussed in details considering also
the relations with the weak field limit. Exact solutions are obtained for
constant Ricci curvature scalar and for Ricci scalar depending on the radial
coordinate. In particular, we discuss how to obtain results which can be
consistently compared with General Relativity giving the well known
post-Newtonian and post-Minkowskian limits. Furthermore, we implement a
perturbation approach to obtain solutions up to the first order starting from
spherically symmetric backgrounds. Exact solutions are given for several
classes of theories in both constant and .Comment: 13 page