A comprehensive analysis of the compact phase space for Hu-Sawicki $f(R)$ dark energy models including spatial curvature

Abstract

We present a comprehensive dynamical systems analysis of homogeneous and isotropic Friedmann-Laîmatre-Robertson-Walker cosmologies in the Hu-Sawicki $f(R)$ dark energy model for the parameter choice $\{n,C_1\}=\{1,1\}$. For a generic $f(R)$ theory, we outline the procedures of compactification of the phase space, which in general is 4-dimensional. We also outline how, given an $f(R)$ model, one can determine the coordinate of the phase space point that corresponds to the present day universe and the equation of a surface in the phase space that represents the $\Lambda$CDM evolution history. Next, we apply these procedures to the Hu-Sawicki model under consideration. We identify some novel features of the phase space of the model such as the existence of invariant submanifolds and 2-dimensional sheets of fixed points. We determine the physically viable region of the phase space, the fixed point corresponding to possible matter dominated epochs and discuss the possibility of a non-singular bounce, re-collapse and cyclic evolution. We also provide a numerical analysis comparing the $\Lambda$CDM evolution and the Hu-Sawicki evolution.

23 pages, 9 figures

References in corpus (13)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Cosmography of f(R) gravity
• The evolution of density perturbations in f(R) gravity
• Some remarks on the dynamical systems approach to fourth order gravity
• Cosmic Jerk, Snap and Beyond
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• Cosmological dynamics of exponential gravity
• Compactifying the state space for alternative theories of gravity
• A Cyclic Universe With Varying Cosmological Constant in $f(R,T)$ gravity
• A model independent approach to the study of $f(R)$ cosmologies with expansion histories close to $\Lambda$CDM
• Cosmology with Hu-Sawicki gravity in Palatini Formalism
• Dynamic properties of cyclic cosmologies

Cited by in corpus (3)

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• Toward Gravitational Lensing in Modified Theories of Gravity
• Unified dynamical system formulations for $f(R,\varphi ,X)$ gravity with applications to nonminimal derivative coupling and $R^2$-Higgs inflation