Thermodynamics and cosmological reconstruction in f(T,B) gravity

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∇μTμ. In this work, we study different features of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology in this theory. First, we show that the FLRW equations can be transformed to the form of Clausius relation TˆhSeff=−dE+WdV, where Tˆh is the horizon temperature and Seff 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 ΛCDM models. Finally, we formulate the perturbed evolution equations and analyse the stability of some important cosmological solutions.