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arXiv · 1202.4057

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

Kazuharu Bamba·Ratbay Myrzakulov·Shin'ichi Nojiri·Sergei D. Odintsov
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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 $T^β$ ($β>1$) 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 $Λ$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.

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Kazuharu Bamba, Ratbay Myrzakulov, Shin'ichi Nojiri, Sergei D. Odintsov. 2012-04-12. Reconstruction of $f(T)$ gravity: Rip cosmology, finite-time future singularities and thermodynamics. https://doi.org/10.1103/physrevd.85.104036

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