Dynamics of f(R)-cosmologies containing Einstein static models

Abstract

We study the dynamics of homogeneous isotropic FRW cosmologies with positive spatial curvature in $f(R)$-gravity, paying special attention to the existence of Einstein static models and only study forms of $f(R)=R^n$ 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.

14 pages, 6 figures

References in corpus (22)

• Extra force in $f(R)$ modified theories of gravity
• The Large Scale Structure of f(R) Gravity
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• Limit to General Relativity in f(R) theories of gravity
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• de Sitter space and the equivalence between f(R) and scalar-tensor gravity
• The evolution of density perturbations in f(R) gravity
• The behavior of $f(R)$ gravity in the solar system, galaxies and clusters
• Cosmological dynamics of Scalar--Tensor Gravity
• Constraints on f(R) Cosmology in the Palatini Formalism
• The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity
• The evolution of cosmological gravitational waves in f(R) gravity
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• The cosmic snap parameter in f(R) gravity
• Cosmological dynamics of exponential gravity
• Perturbative aspects and conformal solutions of F(R) gravity
• Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity
• Compactifying the state space for alternative theories of gravity
• Acceleration of the Universe via f(R) Gravities and The Stability of Extra Dimensions
• Higher Powers in Gravitation
• Curvature Inspired Cosmological Scenario
• An analysis of the shear dynamics in Bianchi I cosmologies with $R^n$-gravity