Some remarks on the dynamical systems approach to fourth order gravity

Abstract

Building on earlier work, we discuss a general framework for exploring the cosmological dynamics of Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a first-order autonomous system and we give several examples which illustrate the utility of our method. We also discuss a number of results which have appeared recently in the literature.

19 pages, LaTeX

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Cited by in corpus (75)

• f(R) Theories Of Gravity
• Modified Gravity and Cosmology
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Dynamical systems applied to cosmology: dark energy and modified gravity
• A Unified Description of Screened Modified Gravity
• On the LCDM Universe in f(R) gravity
• Cosmological dynamics of non-minimally coupled scalar field system and its late time cosmic relevance
• A dynamical system analysis of hybrid metric-Palatini cosmologies
• Phase Space Analysis of the Accelerating Multi-fluid Universe
• Constraining $f(R)$ gravity by the Large Scale Structure
• Modified first-order Horava-Lifshitz gravity: Hamiltonian analysis of the general theory and accelerating FRW cosmology in power-law F(R) model
• An analysis of the phase space of Horava-Lifshitz cosmologies
• Large Scale Structure Constraints for a Class of f(R) Theories of Gravity
• Dynamical analysis on $f(R,\mathcal{G})$ cosmology
• Theoretical and observational constraints of viable f(R) theories of gravity
• Dynamical system analysis for nonminimal torsion-matter coupled gravity
• On the possibility of blue tensor spectrum within single field inflation
• Global gravitational instability of FLRW backgrounds - interpreting the dark sectors
• A detailed analysis of structure growth in $f(R)$ theories of gravity
• Cosmological dynamics of fourth order gravity: A compact view
• Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity
• A Dynamical System Analysis of $f(R,T)$ Gravity
• The Raychaudhuri equation in homogeneous cosmologies
• Anisotropic solutions in f(R) Gravity
• A new approach to the analysis of the phase space of f(R)-gravity
• Qualitative analysis of Kantowski-Sachs metric in a generic class of $f(R)$ models
• Cosmological dynamics of fourth order gravity with a Gauss-Bonnet term
• Generality of Starobinsky and Higgs inflation in the Jordan frame
• Dynamical analysis of generalised $f(R,\mathcal{L})$ theories
• Cosmology of $f(R,\square R)$ gravity
• Chaplygin-gas Solutions of f(R) Gravity
• Searching for dynamical black holes in various theories of gravity
• Phase space of modified Gauss-Bonnet gravity
• The dynamics of Bianchi I universes in $R^n$ cosmologies with torsion
• R^n gravity and the chameleon
• A model independent approach to the study of $f(R)$ cosmologies with expansion histories close to $\Lambda$CDM
• Investigating the accelerated expansion of the Universe through updated constraints on viable $f(R)$ models within the metric formalism
• Dynamical analysis of nonminimal coupled theories
• Stable super-inflating cosmological solutions in f(R)-gravity
• Note on the equation of state of geometric dark-energy in f(R) gravity
• Spatial Curvature in $f(R)$ Gravity
• On tidal forces in f(R) theories of gravity
• New class of generalized coupling theories
• Dynamical equivalence of $f(R)$ gravity in Jordan and Einstein frames
• Signatures of Modified Gravity on the 21-cm Power Spectrum at Reionisation
• Dynamical system analysis of cosmological evolution in the Aether scalar tensor theory
• Cosmological evolution with quadratic gravity and nonideal fluids
• Dynamical reconstruction of the $\Lambda$CDM model in scalar-tensor $f(R,T)$ gravity
• On exponential modified gravity
• On stability of the Kasner solution in quadratic gravity
• About matter and dark-energy domination eras in R^n gravity or lack thereof
• On Shear-free perturbations of f(R) gravity
• A note on the dynamical system formulations in $f(R)$ gravity
• A Born-Infeld-like f(R) gravity
• Asymptotic Properties of a Supposedly Regular (Dirac-Born-Infeld) Modification of General Relativity
• Dynamical properties of Bianchi-I spacetimes in $f(R)$ gravity
• Cosmological dynamics of magnetic Bianchi I in viable $f(R)$ models of gravity
• Non minimally coupled condensate cosmologies: a phase space analysis
• Higher-order gravity in higher dimensions: Geometrical origins of four-dimensional cosmology?
• Dynamical reconstruction of the $\Lambda$CDM model in hybrid metric-Palatini gravity
• Cosmological dynamics in six-order gravity
• Irrotational-fluid cosmologies in fourth-order gravity
• Reconstruction of f(R) gravity models from observations
• Reconstruction of $f(R)$ lagrangian from a massive scalar field
• Late-time power-law stages of cosmological evolution in teleparallel gravity with nonminimal coupling
• A comprehensive analysis of the compact phase space for Hu-Sawicki $f(R)$ dark energy models including spatial curvature
• Late time dynamics of $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ gravity
• A model-independent compact dynamical system formulation for exploring bounce and cyclic cosmological evolutions in $f(R)$ gravity
• Asymptotic solutions in f(R)-gravity
• Cosmological evolutions of $F(R)$ nonlinear massive gravity
• Ten scenarios from early radiation to late time acceleration with a minimally coupled dark energy
• A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge
• Power-Law Bounces in $f(R)$ Gravity: Analysis of the Ekpyrosis and Accelerating Regimes
• $\Lambda$CDM-like evolution in Einstein-scalar-Gauss-Bonnet gravity
• Unified dynamical system formulations for $f(R,\varphi ,X)$ gravity with applications to nonminimal derivative coupling and $R^2$-Higgs inflation