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

Understand

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-low type correction term $T^\beta$ ($\beta>1$) 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 $\Lambda$CDM model, Little Rip cosmology and Pseudo-Rip cosmology.