A note on the dynamical system formulations in $f(R)$ gravity

Abstract

A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in $f(R)$ gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting them in chronological order as they appeared in the history of the relevant scientific literature. In this way, we illuminate how the shortcoming(s) of an existing formulation encouraged the development of an alternative formulation. Whenever possible, a 2-dimensional phase portrait is given for a better visual representation of the dynamics of phase space. We also touch upon how cosmological perturbations can be analyzed using the phase space language.

arXiv comment31 pages. 8 figures. Slight modification done in section 8.1. Invited article for the special issue of IJGMMP dedicated to the conference Geomgrav 2021

References in corpus (31)

• f(R) Theories Of Gravity
• f(R) theories
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Can modified gravity explain accelerated cosmic expansion?
• Conditions for the cosmological viability of f(R) dark energy models
• Dynamical systems applied to cosmology: dark energy and modified gravity
• Cosmological reconstruction of realistic modified F(R) gravities
• Cosmological dynamics of R^n gravity
• Cosmography of f(R) gravity
• On the LCDM Universe in f(R) gravity
• The evolution of density perturbations in f(R) gravity
• f(R) gravity theory and CMBR constraints
• Homogeneous cosmologies with cosmological constant
• The phase space view of f(R) gravity
• Covariant gauge-invariant perturbations in multifluid f(R) gravity
• Some remarks on the dynamical systems approach to fourth order gravity
• Cosmic Jerk, Snap and Beyond
• Dynamics of f(R)-cosmologies containing Einstein static models
• The Existence of Einstein Static Universes and their Stability in Fourth order Theories of Gravity
• Dynamical systems analysis of anisotropic cosmologies in $R^n$-gravity
• A detailed analysis of structure growth in $f(R)$ theories of gravity
• Cosmological dynamics of fourth order gravity: A compact view
• A new approach to the analysis of the phase space of f(R)-gravity
• Revisiting f(R) gravity models that reproduce $\Lambda$CDM expansion
• A model independent approach to the study of $f(R)$ cosmologies with expansion histories close to $\Lambda$CDM
• Correspondence between Jordan-Einstein frames and Palatini-metric formalisms
• Reconstruction of f(R) models with Scale-invariant Power Spectrum
• Dynamical properties of Bianchi-I spacetimes in $f(R)$ gravity
• Covariant and gauge-invariant linear scalar perturbations in multiple scalar field cosmologies
• Reconstruction of f(R) gravity models from observations
• Reconstructing $f(R)$ gravity from the spectral index

Cited by in corpus (9)

• Dynamical systems analysis of $f(Q)$ gravity
• Dynamical systems of modified Gauss-Bonnet gravity: cosmological implications
• Cosmological dynamical systems in modified gravity
• Can $f(R)$ gravity isotropize a pre-bounce contracting universe?
• A generic dynamical system formulation for Bianchi-I cosmology with isotropic fluid in $f(Q)$ gravity
• A model-independent compact dynamical system formulation for exploring bounce and cyclic cosmological evolutions in $f(R)$ gravity
• Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes
• A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge
• Unified dynamical system formulations for $f(R,\varphi ,X)$ gravity with applications to nonminimal derivative coupling and $R^2$-Higgs inflation