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

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 $f(R)=R+m{e}^{[-nR]}$, 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.