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

Understand

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, $B=2\nabla_{\mu}T^{\mu}$.
• In this work, we study different features of a flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) cosmology in this theory.
• First, we show that the FLRW equations can be transformed to the form of Clausius relation $\hat{T}_hS_{\rm eff}=-dE+WdV$, where $\hat{T}_h$ is the horizon temperature and $S_{\rm eff}$ is the entropy which contains contributions both from horizon entropy and an additional entropy term introduced due to the non-equilibrium.