Cosmological Solutions of $f(T)$ Gravity

TL;DR

This paper derives analytical cosmological solutions within $f(T)$ gravity, including isotropic, anisotropic, and vacuum universes, using singularity analysis and exploring conditions for equivalence with general relativity.

Contribution

It introduces a method to find exact solutions in $f(T)$ gravity for various universe models, extending the understanding of teleparallel gravity's cosmological implications.

Findings

Analytical solutions for isotropic and anisotropic universes in $f(T)$ gravity.

Family of Kasner-like solutions in vacuum Bianchi I universe.

Conditions under which $f(T)$ gravity solutions coincide with those of general relativity.

Abstract

In the cosmological scenario in $f\left( T\right) $ gravity, we find analytical solutions for an isotropic and homogeneous universe containing a dust fluid and radiation and for an empty anisotropic Bianchi I universe. The method that we apply is that of movable singularities of differential equations. For the isotropic universe, the solutions are expressed in terms of a Laurent expansion, while for the anisotropic universe we find a family of exact Kasner-like solutions in vacuum. Finally, we discuss when a nonlinear $f\left( T\right) $-gravity theory provides solutions for the teleparallel equivalence of general relativity and derive conditions for exact solutions of general relativity to solve the field equations of an $f(T)$ theory.