Cosmological dynamical systems in modified gravity

Abstract

The field equations of modified gravity theories, when considering a homogeneous and isotropic cosmological model, always become autonomous differential equations. This relies on the fact that in such models all variables only depend on cosmological time, or another suitably chosen time parameter. Consequently, the field equations can always be cast into the form of a dynamical system, a successful approach to study such models. We propose a perspective that is applicable to many different modified gravity models and relies on the standard cosmological density parameters only, making our choice of variables model independent. The drawback of our approach is a more complicated constraint equation. We demonstrate our procedure studying various modified gravity models and show how much generic information can be extracted before a specific model is considered.

arXiv comment19 pages, 6 figures; v2 minor changes, updated references

References in corpus (39)

• Dynamics of dark energy
• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• f(R) theories
• Extended Theories of Gravity
• f(R,T) gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• In the Realm of the Hubble tension $-$ a Review of Solutions
• f(T) teleparallel gravity and cosmology
• Exponential potentials and cosmological scaling solutions
• Curvature Quintessence
• Beyond the Cosmological Standard Model
• Modified teleparallel gravity: inflation without inflaton
• Coincident General Relativity
• Conditions for the cosmological viability of f(R) dark energy models
• Cosmological Tests of Modified Gravity
• Cosmology in $f(Q)$ geometry
• Dynamical systems applied to cosmology: dark energy and modified gravity
• Testing General Relativity in Cosmology
• Observational constraints of $f(Q)$ gravity
• Coupling matter in modified $Q$-gravity
• Challenges to Self-Acceleration in Modified Gravity from Gravitational Waves and Large-Scale Structure
• Observational Tests of Modified Gravity
• Modified Gravity and Cosmology: An Update by the CANTATA Network
• The evidence for a spatially flat Universe
• Viable f(T) models are practically indistinguishable from LCDM
• How isotropic is the Universe?
• Early modified gravity in light of the $H_0$ tension and LSS data
• New observational constraints on f(T) gravity from cosmic chronometers
• Dynamical systems approach and generic properties of $f(T)$ cosmology
• Modified gravity: a unified approach
• Updating constraints on f(T) teleparallel cosmology and the consistency with Big Bang Nucleosynthesis
• On dynamical systems approaches and methods in $f(R)$ cosmology
• Cosmological phase space of generalized hybrid metric-Palatini theories of gravity
• A new approach to the analysis of the phase space of f(R)-gravity
• Parametrizations for tests of gravity
• A note on the dynamical system formulations in $f(R)$ gravity

Cited by in corpus (13)

• Dynamical systems analysis of $f(Q)$ gravity
• Spherically symmetric teleparallel geometries
• Generalized Teleparallel de Sitter geometries
• Cosmological fluids with boundary term couplings
• A generic dynamical system formulation for Bianchi-I cosmology with isotropic fluid in $f(Q)$ gravity
• Accelerating behavior from dynamical system analysis parameters
• Phase space analysis of an exponential model in $f(Q)$ gravity including linear dark-sector interactions
• A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge
• Absence of curvature singularities in symmetric perfect fluid spacetimes in Einstein-Gauss-Bonnet Gravity
• Onset of dark energy from cosmological scalarization and gravitational wave speed
• Cosmological dynamical systems of non-minimally coupled fluids and scalar fields
• Geometric formulation of $k$-essence and late-time acceleration
• Stability Analysis of Four $f(Q)$ Gravity Models : A Cosmological Review in the Background of Bianchi-I Anisotropy