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.

19 pages, 6 figures; v2 minor changes, updated references

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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