Dynamics of the anisotropic Kantowsky-Sachs geometries in $R^n$ gravity

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Abstract

We construct general anisotropic cosmological scenarios governed by an $f(R)$ gravitational sector. Focusing then on Kantowski-Sachs geometries in the case of $R^n$-gravity, and modelling the matter content as a perfect fluid, we perform a detailed phase-space analysis. We find that at late times the universe can result to a state of accelerating expansion, and additionally, for a particular $n$-range ($2<n<3$) it exhibits phantom behavior. Furthermore, isotropization has been achieved independently of the initial anisotropy degree, showing in a natural way why the observable universe is so homogeneous and isotropic, without relying on a cosmic no-hair theorem. Moreover, contracting solutions have also a large probability to be the late-time states of the universe. Finally, we can also obtain the realization of the cosmological bounce and turnaround, as well as of cyclic cosmology. These features indicate that anisotropic geometries in modified gravitational frameworks present radically different cosmological behaviors comparing to the simple isotropic scenarios.

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Dynamics of dark energy

M. Sami, Edmund J. Copeland, Shinji Tsujikawa (2006)

In this paper we review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating Universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

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f(R) Theories Of Gravity

Thomas Sotiriou, Valerio Faraoni (2008)

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology and astrophysics. Among numerous alternatives to Einstein's theory of gravity, theories which include higher order curvature invariants, and specifically the particular class of f(R) theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. We review here f(R) theories of gravity in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented -- metric, Palatini and metric-affine -- and the following topics are discussed: motivation; actions, field equations and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; astrophysical applications.