Energy Conditions in $f(\mathcal{G},T)$ Gravity

Abstract: The aim of this paper is to introduce a new modified gravity theory named as $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ are the Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively) and investigate energy conditions for two reconstructed models in the context of FRW universe. We formulate general field equations, divergence of energy-momentum tensor, equation of motion for test particles as well as corresponding energy conditions. The massive test particles follow non-geodesic lines of geometry due to the presence of extra force. We express energy conditions in terms of cosmological parameters like deceleration, jerk and snap parameters. The reconstruction technique is applied to this theory using de Sitter and power-law cosmological solutions. We analyze energy bounds and obtain feasible constraints on free parameters.