Stability of the Kasner Universe in f(T) Gravity

TL;DR

This paper analyzes the stability of the Kasner universe within $f(T)$ gravity, revealing that the Kasner solution is unstable and that the universe tends toward a de Sitter state due to $f(T)$ effects.

Contribution

It investigates the stability of anisotropic Kasner solutions in $f(T)$ gravity and shows the late-time dominance of de Sitter space driven by $f(T)$ modifications.

Findings

Kasner solution is a saddle point and unstable.

De Sitter universe acts as a late-time attractor.

$f(T)$ contributions facilitate isotropization.

Abstract

$f(T)$ gravity offers an alternative context in which to consider gravitational interactions where torsion, rather than curvature, is the mechanism by which gravitation is communicated. We investigate the stability of the Kasner solution with several forms of the arbitrary lagrangian function examined within the $f(T)$ context. This is a Bianchi type--I vacuum solution with anisotropic expansion factors. In the $f(T)$ gravity setting, the solution must conform to a set of conditions in order to continue to be a vacuum solution of the generalized field equations. With this solution in hand, the perturbed field equations are determined for power-law and exponential forms of the $f(T)$ function. We find that the point which describes the Kasner solution is a saddle point which means that the singular solution is unstable. However, we find the de Sitter universe is a late-time attractor. In general relativity, the cosmological constant drives the the isotropization of the spacetime while in this setting the extra $f(T)$ contributions now provide this impetus.