Testing some f(R,T) gravity models from energy conditions

We consider $f(R, T)$ theory of gravity, where $R$ is the curvature scalar and $T$ the trace of the energy momentum tensor. Attention is attached to the special case, $f(R, T)= R+2f(T)$ and two expressions are assumed for the function $f(T)$, $\frac{a_1T^n+b_1}{a_2T^n+b_2}$ and $a_3\ln^{q}{(b_3T^m)}$, where $a_1$, $a_2$, $b_1$, $b_2$, $n$, $a_3$, $b_3$, $q$ and $m$ are input parameters. We observe that by adjusting suitably these input parameters, energy conditions can be satisfied. Moreover, an analyse of the perturbations and stabilities of de Sitter solutions and power-law solutions is performed with the use of the two models. The results show that for some values of the input parameters, for which energy conditions are satisfied, de Sitter solutions and power-law solutions may be stables.