Reconstruction off(T)gravity: Rip cosmology, finite-time future singularities, and thermodynamics

Abstract

We demonstrate that there appear finite-time future singularities in $f(T)$ gravity with $T$ being the torsion scalar. We reconstruct a model of $f(T)$ gravity with realizing the finite-time future singularities. In addition, it is explicitly shown that a power-law-type correction term ${T}^{\ensuremath{\beta}}$ ($\ensuremath{\beta}>1$) such as a ${T}^{2}$ term can remove the finite-time future singularities in $f(T)$ gravity. Moreover, we study $f(T)$ models with realizing inflation in the early universe, the $\ensuremath{\Lambda}\mathrm{CDM}$ model, little rip cosmology and pseudo-rip cosmology. It is demonstrated that the disintegration of bound structures for little rip and pseudo-rip cosmologies occurs in the same way as in gravity with corresponding dark energy fluid. We also discuss that the time-dependent matter instability in the star collapse can occur in $f(T)$ gravity. Furthermore, we explore thermodynamics in $f(T)$ gravity and illustrate that the second law of thermodynamics can be satisfied around the finite-time future singularities for the universe with the temperature inside the horizon being the same as that of the apparent horizon.