Anisotropic cosmological solutions in $R+R^2$ gravity

Abstract

In this paper we investigate the past evolution of an anisotropic Bianchi I universe in $R+R^2$ gravity. Using the dynamical system approach we show that there exists a new two-parameters set of solutions that includes both an isotropic "false radiation" solution and an anisotropic generalized Kasner solution, which is stable. We derive the analytic behaviour of the shear from a specific property of $f(R)$ gravity and the analytic asymptotic form of the Ricci scalar when approaching the initial singularity. Finally we numerically checked our results.

arXiv comment13 pages, 2 figures

References in corpus (25)

• f(R) Theories Of Gravity
• Curvature Quintessence
• Disappearing cosmological constant in f(R) gravity
• Are f(R) dark energy models cosmologically viable ?
• Anisotropically Inflating Universes
• On the evolution of universes in quadratic theories of gravity
• Modified gravity as an alternative for Lambda-CDM cosmology
• From stable to unstable anomaly-induced inflation
• Simple Types of Anisotropic Inflation
• On dynamical systems approaches and methods in $f(R)$ cosmology
• On The Existence Of Anisotropic Cosmological Models In Higher-Order Theories Of Gravity
• Induced gravity, and minimally and conformally coupled scalar fields in Bianchi-I cosmological models
• Stable Isotropic Cosmological Singularities in Quadratic Gravity
• The Stability of an Isotropic Cosmological Singularity in Higher-Order Gravity
• Proof of the Cosmic No-Hair Conjecture for Quadratic Homogeneous Cosmologies
• Dynamical system approach to FRW models in higher-order gravity theories
• Asymptotics of flat, radiation universes in quadratic gravity
• On stability of the Kasner solution in quadratic gravity
• Slice Energy in Higher Order Gravity Theories and Conformal Transformations
• Oscillatory behavior of closed isotropic models in second order gravity theory
• Numerical Bianchi I solutions in semi-classical gravitation
• About Starobinsky inflation
• Bianchi $VI{I}_A$ solutions of quadratic gravity
• Bianchi I solutions of effective quadratic gravity
• Homogeneous Solutions of Quadratic Gravity

Cited by in corpus (44)

• Teleparallel Gravity: From Theory to Cosmology
• Traversable Wormholes and Energy Conditions with Two Different Shape Functions in $f(R)$ Gravity
• Traversable Wormholes in $R+\alpha R^n$ Gravity
• Non violation of energy conditions in wormholes modelling
• Anisotropy screening in Horndeski cosmologies
• No-go theorem for inflation in Ricci-inverse gravity
• Cosmological consequences of a principle of finite amplitudes
• No-go theorem for inflation in an extended Ricci-inverse gravity model
• On Kasner solution in Bianchi I $f(T)$ cosmology
• Traversable wormhole in logarithmic $f(R)$ gravity by various shape and redshift functions
• On the initial singularity and extendibility of flat quasi-de Sitter spacetimes
• Generalized non-local $R^2$-like inflation
• Morris-Thorne-type wormhole with global monopole charge and the energy conditions
• Integrable modified gravity cosmological models with an additional scalar field
• An anisotropic bouncing universe in non-local gravity
• Anisotropic constant-roll inflation for the Dirac-Born-Infeld model
• Superpotential method for $F(R)$ cosmological models
• Dynamical properties of Bianchi-I spacetimes in $f(R)$ gravity
• Beyond the linear analysis of stability in higher derivative gravity with the Bianchi-I metric
• Anisotropic power-law inflation for a model of two scalar and two vector fields
• Stable small spatial hairs in a power-law k-inflation model
• Anisotropic Massive Gauge-flation
• CMB imprints of non-canonical anisotropic inflation
• Non-local Starobinsky inflation in the light of future CMB
• Stability investigations of isotropic and anisotropic exponential inflation in the Starobinsky-Bel-Robinson gravity
• Bouncing Cosmological Isotropic Solutions in Scalar-Tensor Gravity
• Primordial flat frame -- a new view on inflation
• Some aspects of the cosmological dynamics in Einstein-Gauss-Bonnet gravity
• Nonlinear anisotropy growth in Bianchi-I spacetime in metric $f(R)$ cosmology
• Anisotropic chiral cosmology: exact solutions
• Anisotropic hyperbolic inflation for a model of two scalar and two vector fields
• Splitting into two isotropic subspaces as a result of cosmological evolution in Einstein-Gauss-Bonnet gravity
• Anisotropic Born-Infeld-f(R) Cosmologies
• Quantum Hubble horizon
• Anisotropic cosmological dynamics in Einstein-Gauss-Bonnet gravity: an example of dynamical compactification in 7+1 dimensions
• Quantum fields in Bianchi type I spacetimes. The Kasner metrc
• Anisotropic solutions for $R^2$ gravity model with a scalar field
• Viable Anisotropic Inflation and Reheating in the Tachyon Model
• Stability investigations of de Sitter inflationary solutions in power-law extensions of the Starobinsky model
• Anisotropic cosmology in $q$-deformed entropic gravity
• Static cosmological solutions in quadratic gravity
• Density perturbation and cosmological evolution in the presence of magnetic field in $f(R)$ gravity models
• Observational Viability of Anisotropic Inflation Revisited
• Bounce and stability in the early cosmology with anomaly-induced corrections