Reconstruction of cosmological models in a general gravitational framework involving torsion scalar

Abstract

This study is elaborated to reconstruct some cosmological models in the gravitational framework of an extended teleparallel gravity based on the higher-order derivative terms of torsion scalar. To achieve this goal, we consider spatially flat FRW model with perfect fluid as background matter distribution. In this framework, we find some interesting exact solutions by using the hybrid and intermediate forms of scale factor via a well-known reconstruction scheme. For exploring physical significance of the reconstructed solutions, we analyze the behavior of dark energy EoS parameter, the validity of energy condition bounds as well as the generalized second law of thermodynamics graphically. For investigating the stability of reconstructed solutions, we check the behavior of speed of sound [Formula: see text] in each case. It is seen that in de Sitter case, the reconstruction of full Lagrangian function is not possible as it reduces to the case of simple [Formula: see text] gravity which has already been discussed in literature. While for power law form of scale factor, it is found that reconstruction is possible and most of the obtained solutions favor the quintessence era of cosmic evolution. Further, it is concluded that both the energy conditions and generalized second thermodynamical law hold for the reconstructed solutions and these solutions exhibit stable behavior (as [Formula: see text]). Lastly, in case of intermediate form of scale factor, the resulting differential equations are very complicated and hence the analytical solution is possible only for the simplest case which, further, indicates cosmologically promising behavior.