Energy Conditions Constraints and Stability of Power Law Solutions in f(R,T) Gravity

Abstract: The energy conditions are derived in the context of $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor, which can reduce to the well-known conditions in $f(R)$ gravity and general relativity. We present the general inequalities set by the energy conditions in terms of Hubble, deceleration, jerk and snap parameters. In this study, we concentrate on two particular models of $f(R,T)$ gravity namely, $f(R)+\lambda{T}$ and $R+2f(T)$. The exact power-law solutions are obtained for these two cases in homogeneous and isotropic $f(R,T)$ cosmology. Finally, we find certain constraints which have to be satisfied to ensure that power law solutions may be stable and match the bounds prescribed by the energy conditions.