Thermodynamics and cosmological reconstruction inf(T,B)gravity

Abstract

Abstract Recently, it was formulated a teleparallel theory called f ( T , B ) gravity which connects both f ( T ) and f ( R ) under suitable limits. In this theory, the function in the action is assumed to depend on the torsion scalar T and also on a boundary term related with the divergence of torsion, B = 2 ∇ μ T μ . In this work, we study different features of a flat Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmology in this theory. First, we show that the FLRW equations can be transformed to the form of Clausius relation T ˆ h S eff = − d E + W d V , where T ˆ h is the horizon temperature and S eff is the entropy which contains contributions both from horizon entropy and an additional entropy term introduced due to the non-equilibrium. We also formulate the constraint for the validity of the generalised second law of thermodynamics (GSLT). Additionally, using a cosmological reconstruction technique, we show that both f ( T , B ) and − T + F ( B ) gravity can mimic power-law, de-Sitter and Λ CDM models. Finally, we formulate the perturbed evolution equations and analyse the stability of some important cosmological solutions.