A new approach to the analysis of the phase space of f(R)-gravity

Abstract

We propose a new dynamical system formalism for the analysis of f(R) cosmologies. The new approach eliminates the need for cumbersome inversions to close the dynamical system and allows the analysis of the phase space of f(R)-gravity models which cannot be investigated using the standard technique. Differently form previously proposed similar techniques, the new method is constructed in such a way to associate to the fixed points scale factors, which contain four integration constants (i.e. solutions of fourth order differential equations). In this way a new light is shed on the physical meaning of the fixed points. We apply this technique to some f(R) Lagrangians relevant for inflationary and dark energy models.

32 pages, 13 figures, typos corrected, updated bibliography

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Cited by in corpus (28)

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• Dynamical systems approach and generic properties of $f(T)$ cosmology
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• Dynamical system analysis for nonminimal torsion-matter coupled gravity
• Cosmological dynamics of scalar fields with kinetic corrections: Beyond the exponential potential
• Cosmology of $f(R,\square R)$ gravity
• Phase space of modified Gauss-Bonnet gravity
• Dynamical systems analysis of $f(Q)$ gravity
• Dynamical analysis of interacting dark energy model in the framework of particle creation mechanism
• A model independent approach to the study of $f(R)$ cosmologies with expansion histories close to $\Lambda$CDM
• Cosmological dynamical systems in modified gravity
• New class of generalized coupling theories
• Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames
• Dynamical system analysis of cosmological evolution in the Aether scalar tensor theory
• Dynamical reconstruction of the $\Lambda$CDM model in scalar-tensor $f(R,T)$ gravity
• A note on the dynamical system formulations in $f(R)$ gravity
• Cosmological dynamics of magnetic Bianchi I in viable $f(R)$ models of gravity
• Dynamical properties of Bianchi-I spacetimes in $f(R)$ gravity
• Dynamical system analysis of LRS-BI Universe with f(Q) gravity theory
• Dynamical reconstruction of the $\Lambda$CDM model in hybrid metric-Palatini gravity
• Reconstruction of the singularity-free $f(\mathcal{R})$ gravity via Raychaudhuri equations
• A comprehensive analysis of the compact phase space for Hu-Sawicki $f(R)$ dark energy models including spatial curvature
• Viability of Arctan Model of f(R) Gravity for Late-time Cosmology
• A New f(R) Model in the Light of Local Gravity Test and Late-time Cosmology
• New dynamical system approach to Palatini $f(R)$ theories and its application to exponential gravity
• $\Lambda$CDM-like evolution in Einstein-scalar-Gauss-Bonnet gravity
• Phase space analysis of Bianchi III Universe with $f(R,T)$ gravity theory