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

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.