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

TL;DR

This paper investigates finite-time future singularities in $f(T)$ gravity, reconstructs models to realize these singularities, shows how certain corrections can remove them, and explores implications for cosmology, thermodynamics, and star collapse.

Contribution

It provides a reconstruction of $f(T)$ gravity models with finite-time singularities and demonstrates how power-law corrections can eliminate these singularities, extending understanding of $f(T)$ cosmologies.

Findings

Finite-time future singularities can occur in $f(T)$ gravity.

Power-law correction terms like $T^2$ can remove singularities.

The second law of thermodynamics holds near singularities under certain conditions.

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-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. 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.