$f(R,T)=f(R)+\lambda T$ gravity models as alternatives to cosmic acceleration

TL;DR

This paper explores specific $f(R,T)$ gravity models with fixed trace dependence, deriving cosmological solutions and analyzing their potential as alternatives to cosmic acceleration.

Contribution

It introduces new $f(R,T)$ models with fixed $T$-dependence and derives exact cosmological solutions under a hybrid expansion law.

Findings

Different $f(R)$ functions lead to varied cosmological behaviors.

Adding the trace term influences the universe's expansion dynamics.

Om diagnostic analysis distinguishes these models from standard cosmology.

Abstract

This article presents cosmological models that arise in a subclass of $f(R,T)=f(R)+f(T)$ gravity models, with different $f(R)$ functions and fixed $T$-dependence. That is, the gravitational lagrangian is considered as $f(R,T)=f(R)+\lambda T$, with constant $\lambda$. Here $R$ and $T$ represent the Ricci scalar and trace of the stress-energy tensor, respectively. The modified gravitational field equations are obtained through the metric formalism for the Friedmann-Lema\^itre-Robertson-Walker metric with signature $(+,-,-,-)$. We work with $f(R)=R+\alpha R^2-\frac{\mu^4}{R}$, $f(R)=R+k\ln(\gamma R)$ and $f(R)=R+me^{[-nR]}$, with $\alpha, \mu, k, \gamma, m$ and $n$ all free parameters, which lead to three different cosmological models for our Universe. For the choice of $\lambda=0$, this reduces to widely discussed $f(R)$ gravity models. This manuscript clearly describes the effects of adding the trace of the energy-momentum tensor in the $f(R)$ lagrangian. The exact solution of the modified field equations are obtained under the hybrid expansion law. Also we present the Om diagnostic analysis for the discussed models.