Shear dynamics in Bianchi I cosmologies with R^n-gravity

Abstract

We give the equations governing the shear evolution in Bianchi spacetimes for general f(R)-theories of gravity. We consider the case of R^n-gravity and perform a detailed analysis of the dynamics in Bianchi I cosmologies which exhibit local rotational symmetry. We find exact solutions and study their behaviour and stability in terms of the values of the parameter n. In particular, we found a set of cosmic histories in which the universe is initially isotropic, then develops shear anisotropies which approaches a constant value.

25 pages LaTeX, 6 figures. Revised to match the final version accepted for publication in CQG

References in corpus (1)

• Further Exact Cosmological Solutions to Higher-Order Gravity Theories

Cited by in corpus (64)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• Dynamical systems applied to cosmology: dark energy and modified gravity
• Dark matter as a geometric effect in f(R) gravity
• Stability of the Einstein static universe in f(R) gravity
• On the evolution of universes in quadratic theories of gravity
• The phase space view of f(R) gravity
• Exact solutions of f(R) gravity coupled to nonlinear electrodynamics
• Cosmological dynamics of Scalar--Tensor Gravity
• Dynamical analysis of anisotropic scalar-field cosmologies for a wide range of potentials
• Spherically Symmetric Solutions to Fourth-Order Theories of Gravity
• Dynamics of the anisotropic Kantowsky-Sachs geometries in $R^n$ gravity
• Dynamics of f(R)-cosmologies containing Einstein static models
• A dynamical system analysis of hybrid metric-Palatini cosmologies
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• The Parameterised Post-Newtonian Limit of Fourth-Order Theories of Gravity
• Large Scale Structure Constraints for a Class of f(R) Theories of Gravity
• Cosmological dynamics of exponential gravity
• Dynamical system analysis for nonminimal torsion-matter coupled gravity
• Global gravitational instability of FLRW backgrounds - interpreting the dark sectors
• Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory
• A detailed analysis of structure growth in $f(R)$ theories of gravity
• Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity
• Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
• Anisotropic solutions in f(R) Gravity
• The Raychaudhuri equation in homogeneous cosmologies
• A new approach to the analysis of the phase space of f(R)-gravity
• Qualitative analysis of Kantowski-Sachs metric in a generic class of $f(R)$ models
• On $f(R)$ gravity in scalar-tensor theories
• Compactifying the state space for alternative theories of gravity
• Asymptotic behavior of a scalar field with an arbitrary potential trapped on a Randall-Sundrum's braneworld: the effect of a negative dark radiation term on a Bianchi I brane
• Cosmology of $f(R,\square R)$ gravity
• A dynamical system approach to higher order gravity
• Searching for dynamical black holes in various theories of gravity
• Phase space of modified Gauss-Bonnet gravity
• Chaplygin-gas Solutions of f(R) Gravity
• R^n gravity and the chameleon
• The dynamics of Bianchi I universes in $R^n$ cosmologies with torsion
• Higher Powers in Gravitation
• New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gas
• Exact Friedmann Solutions in Higher-Order Gravity Theories
• On tidal forces in f(R) theories of gravity
• New class of generalized coupling theories
• Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames
• Dynamical system approach of non-minimal coupling in AdS/CFT cosmology
• On Shear-free perturbations of f(R) gravity
• De Sitter stability in quadratic gravity
• Cosmological dynamics of magnetic Bianchi I in viable $f(R)$ models of gravity
• Dynamical properties of Bianchi-I spacetimes in $f(R)$ gravity
• Phase Space of Anisotropic $R^n$ Cosmologies
• f(R) Gravity in an Ellipsoidal Universe
• Non minimally coupled condensate cosmologies: a phase space analysis
• Perfect fluid solutions of Brans-Dicke and f(R)cosmology
• Irrotational-fluid cosmologies in fourth-order gravity
• Covariant gauge invariant theory of Scalar Perturbations in $f(R)$-gravity: a brief review
• Reconstruction of $f(R)$ lagrangian from a massive scalar field
• A comprehensive analysis of the compact phase space for Hu-Sawicki $f(R)$ dark energy models including spatial curvature
• Vacuum self similar anisotropic cosmologies in $F(R)-$gravity
• Exact analytical vacuum solutions of $R^n$-gravity model depending on two variables
• Cosmological Singularity and Power-Law Solutions in Modified Gravity
• Effect of bulk Lorentz violation on anisotropic brane cosmologies
• Density perturbation and cosmological evolution in the presence of magnetic field in $f(R)$ gravity models
• Scheme of integration of vacuum $F(R)$ gravity in a travelling wave variable