We study an interesting alternative of modified gravity theory, namely, the unimodular f (R, T ) gravity in which R is the Ricci scalar and T is the trace of the stress– energy tensor. We study the viability of the model by using the energy conditions.We discuss the strong, weak, null and dominant energy conditions in terms of deceleration, jerk and snap parameters. We investigate energy conditions for reconstructed unimodular f (R, T ) models and give some constraints on the parametric space of themodel.We observe that by setting appropriately free parameters, energy conditions can be satisfied. Furthermore, we study the stability of the solutions in perturbations framework. In this case, we investigate stability conditions for de Sitter and power law solutions and we examine viability of cosmological evolution of these perturbations. The results show that for some values of the input parameters, for which energy conditions are satisfied, de Sitter and power-lawsolutions may be stable.
