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

TL;DR

The paper investigates cosmic acceleration within the matter–geometry coupling framework of $f(R,L_m,T)$ gravity, focusing on the specific model $f(R,L_m,T)=R- L_m T-$ with $L_m=-\rho$ in a flat FLRW universe. By deriving the modified Friedmann equations and recasting the dynamics as a 3D autonomous system with $x+y+z=1$, the authors identify five critical points and analyze their stability to map the cosmic evolution. A robust de Sitter attractor is found at $D=(1,0,0)$, indicating a late-time accelerating phase, while other points correspond to early-time or transient behaviors; present-day values $\omega_{ ext{tot}}(z=0)\approx -1\pm 0.2$ and $q(z=0)\approx -0.82$ align with Planck measurements. Overall, the work demonstrates that matter–geometry coupling in this $f(R,L_m,T)$ framework can naturally drive a transition from deceleration to acceleration without invoking a separate cosmological constant.

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 $f(R,L_m,T) = R - μL_m T - γ$, with $μ$ and $γ$ being positive constants. The matter sector is characterized by the Lagrangian density $L_m = -ρ$, where $ρ$ 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.

Figures (2)

• Figure 1: 3D plot phase space to analyse the behaviour of phase space trajectories.
• Figure 2: Behaviour of EoS and deceleration parameters, the initial conditions are $x_0=10^{-8.89},y_0=10^{-4},z_0=\sqrt{0.999}$.