Dynamical Systems Analysis of $f(R,L_m)$ Gravity Model

Abstract

In this article, we examine the dynamical evolution of flat FRW cosmological model in $f(R,L_m)$ gravity theory. We consider the general form of $f(R,L_m)$ defined as $f(R,L_m)=\Lambda +\frac{\alpha }{2}R+\beta L_m^n$, where $\Lambda$, $\alpha$, $\beta$, $n$ are model parameters, with the matter Lagrangian given by $L_m=-p$. We investigate the model through phase plane analysis, actively studying the evolution of cosmological solutions using dynamical systems techniques. To analyse the evolution equations, we introduce suitable transformations of variables and discuss the corresponding solutions by phase-plane analysis. The nature of critical points is analysed and stable attractors are examined for $f(R,L_m)$ gravity cosmological model. We examine the linear and classical stability of the model and discuss it in detail. Further, we investigate the transition stage of the Universe, i.e. from the early decelerating stage to the present accelerating phase of the Universe by evolution of the effective equation of state, $\{r,s\}$ parameters and statefinder diagnostics for the central values of parameters $\alpha ,\beta$ and $n$ constrained using MCMC technique with cosmic chronometer data.

22 pages, 14 figures

References in corpus (48)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• emcee: The MCMC Hammer
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• 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
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Statefinder -- a new geometrical diagnostic of dark energy
• Disappearing cosmological constant in f(R) gravity
• Properties of singularities in (phantom) dark energy universe
• Extra force in $f(R)$ modified theories of gravity
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• f(R,L_m) gravity
• Unifying inflation with LambdaCDM epoch in modified f(R) gravity consistent with Solar System tests
• Are f(R) dark energy models cosmologically viable ?
• Dynamical systems applied to cosmology: dark energy and modified gravity
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Extended Gravity Cosmography
• Modified gravity with arbitrary coupling between matter and geometry
• Generalized curvature-matter couplings in modified gravity
• Cosmological dynamics of R^n gravity
• Solar system and equivalence principle constraints on f(R) gravity by chameleon approach
• Energy conditions in f(R)-gravity
• Phantom crossing, equation-of-state singularities, and local gravity constraints in f(R) models
• Cosmography of f(R) gravity
• The Lagrangian description of perfect fluids and modified gravity with an extra force
• Solar System experiments do not yet veto modified gravity models
• Energy conditions in $f(R,L_m)$ gravity
• Gravitational induced particle production through a nonminimal curvature-matter coupling
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• A viability criterion for modified gravity with an extra force
• Matter density perturbations in modified gravity models with arbitrary coupling between matter and geometry
• Galactic rotation curves in modified gravity with non-minimal coupling between matter and geometry
• New observational constraints on $f(R)$ gravity from cosmic chronometers
• The behavior of $f(R)$ gravity in the solar system, galaxies and clusters
• Finite-time Cosmological Singularities and the Possible Fate of the Universe
• Constraining f(R) gravity in solar system, cosmology and binary pulsar systems
• Bounce behaviour in Kantowski-Sachs and Bianchi Cosmologies
• Cosmology from non-minimal geometry-matter coupling
• Late-time constraints on modified Gauss-Bonnet cosmology
• Compactifying the state space for alternative theories of gravity
• The Early-time Cosmology with Stiff Era from Modified Gravity
• Stiff Matter Solution in Brans-Dicke Theory and The General Relativity Limit
• Exact Kantowski-Sachs spacetimes in Einstein-Aether Scalar field theory
• Collapsing scenario for the k-essence emergent generalised Vaidya spacetime in the context of massive gravity's rainbow

Cited by in corpus (1)

• Cosmological model with Gong-Zong Parametrization in $f(R,L_m)$ gravity