Cosmological evolution in f(R,Lm,T) gravity with viscosity

Abstract

We investigate the cosmological evolution of $f(R,L_m,T)$ gravity, a theory that unifies $f(R,T)$ and $f(R,L_m)$ by considering a gravitational Lagrangian depending on the Ricci scalar $R$, the matter Lagrangian $L_m$, and the trace $T$ of the energy–momentum tensor. Focusing on the linear model $f(R,L_m,T)=R+\alpha L_m+\beta T$ and introducing a bulk viscous pressure $p_v=-3\zeta H$, we constrain the model using cosmic chronometers, PantheonPlus+SH0ES, and BAO datasets. We analyze the evolution of $H\left(z\right)$, $q\left(z\right)$, $\rho \left(z\right)$, and $\omega \left(z\right)$, finding a transition from deceleration to acceleration around $z_t\sim 1$, and a shift from matter-like to dark energy-like behavior at low redshifts. The $Om\left(z\right)$ diagnostic reveals deviations from $\Lambda$CDM, confirming a quintessence-like behavior. Our results highlight that viscosity and non-minimal couplings offer a viable mechanism for explaining the late-time acceleration of the universe.