Cosmological Dynamics in $f(R,L_m,T)$ Modified Gravity

TL;DR

This paper explores the accelerating expansion of the universe within a specific $f(R,L_m,T)$ gravity model, analyzing its dynamics and critical points to understand the transition from deceleration to acceleration.

Contribution

It introduces a novel $f(R,L_m,T)$ gravity model with phase space analysis to study cosmic acceleration and transition phases.

Findings

Identification of stable attractors in the cosmological phase space

Demonstration of transition from decelerating to accelerating universe

Analysis of the equation of state and deceleration parameter behaviors

Abstract

In this paper, we investigate the accelerating phase of the Universe within the context of $f(R,L_m,T)$ gravity theory, where $R$, $L_m$, and $T$ represent the Ricci scalar, matter Lagrangian, and the trace of the energy-momentum tensor, respectively. We focus on a particular form of modified gravity defined by $f(R,L_m,T) = R - \mu L_m T - \gamma$, with $\mu$ and $\gamma$ being positive constants. The matter sector is characterized by the Lagrangian density $L_m = -\rho$, where $\rho$ denotes the energy density of the cosmological fluid. We conduct an in-depth examination of the model using phase space analysis, thoroughly evaluating the evolution of cosmological solutions with dynamical system techniques. The results is illustrated through graphs in the phase space, the characteristics of critical points and the stable attractors within the proposed modified gravity $f(R,L_m,T)$ cosmological framework. We investigate the transition from the initial decelerating phase of the universe to its current accelerating phase. The behaviour of the EoS, deceleration parameter with the appropriate initial conditions have been investigated.