Generalized second law of thermodynamics in $f(T,T_{G})$ gravity

Abstract

We discuss the equilibrium picture of thermodynamic at the apparent horizon of FRW universe in $f(T,T_{G})$ gravity, where $T$ represents the torsion invariant and $T_{G}$ is the teleparallel equivalent of the Gauss-Bonnet term. It is found that one can translate the Friedmann equations to the standard form of first law of thermodynamics. We discuss GSLT in the locality of assumption that temperature of matter inside the horizon is similar to that of apparent horizon. Furthermore, we consider particular models in this theory and generate constraints on the coupling parameters for the validity of GSLT. For this purpose we set the present day values of cosmic parameters and find the possible constraints on $f(T,T_{G})$ models. We also choose the power law cosmology and found that GSLT can be met in accelerated cosmic expansion. We have also presented the cosmological reconstruction of some viable $f(T,T_{G})$ models and discussed the cosmic evolution and validity of GSLT.