Energy Constraints and $F(T,T_{G})$ Cosmology

The present paper is elaborated to discuss the energy condition bounds in a modified teleparallel gravity namely $F(T,T_{G})$, involving torsion invariant $T$ and contribution from a term $T_G$, the teleparallel equivalent of the Gauss-Bonnet term. For this purpose, we consider flat FRW universe with matter contents as perfect fluid. We formulate the SEC, NEC, WEC and DEC in terms of some cosmic parameters including Hubble, deceleration, jerk and snap parameters. By taking two interesting models for $F(T,T_{G})$ and some recent limits of these cosmic parameters, we explore the constraints on the free parameters present in both assumed models. We also discuss these constraints graphically in terms of cosmic time by taking power law cosmology into account.