Dynamical System Analysis of FLRW Model in f(R,L,T) Theory

TL;DR

This work addresses cosmic acceleration within the modified gravity framework of $f(R,L,T)$ gravity, focusing on the additive coupling $f(R,L,T)=R+\alpha L+\beta T$ in a flat FLRW background. It introduces a canonical scalar field with an exponential potential and constructs a dimensionless autonomous system using $x_1^2$, $x_2^2$, $x_3^2$, $x_4^2$ under the constraint $1= x_1^2+x_2^2+x_3^2+x_4^2$. The dynamical-system analysis yields eight fixed points $A^{\pm},B^{\pm},C^{\pm},D^{\pm}$ whose cosmological roles span matter-dominated, scalar-field-dominated, and dark-energy-dominated evolutions, with explicit expressions for $q$ and $\omega_{eff}$. Stability properties of these points illustrate viable cosmic histories within this coupling and highlight the impact of geometry–matter coupling on late-time acceleration.

Abstract

Modified gravity theories have been extensively studied recently as viable substitutes for general relativity to deal with cosmological issues like dark energy and late-time cosmic acceleration. In the present work, we investigate the dynamical behavior of the $f(R,L,T)$ gravity model with a scalar field utilizing exponential potential, where $R$ represents the Ricci scalar, $L$ is the Lagrangian density and $T$ is the trace of the energy-momentum tensor. We concentrate on a specific type of modified gravity characterized by $f(R,L,T) =R+αL+βT$, where $α$ and $β$ are positive constants. We study the dynamical behavior and late-time evolution of a cosmological model using a thorough phase-space analysis. We assess important cosmological parameters at the critical places, such as the density parameters corresponding to various cosmic components, the deceleration parameter, and the effective equation of state parameter. The nature of the cosmic phases such as matter-dominated, radiation-dominated, and accelerated expansion eras, described using these quantities.