Stability of the Kasner universe in f(T) gravity

Abstract

f (T ) gravity theory 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.PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x

On Kasner solution in Bianchi I f(T) cosmology

“…On the contrary, Ref. [27] claims that a Kasner solution is still a solution for f (T ) theory, though it is unstable. The fact that the Kasner solution remains as a solution can easily be checked by direct substitution to the equations of motion.…”

“…This strategy has been implemented recently in several papers [24][25][26][27]. The resulting equations of motion appear to be nonpathological.…”

“…So, the statement that the Kasner solution satisfies the equations of motion in f (T ) theory made in the Introduction of [27], and the statement that it is unstable (which is the [27]) are both correct only when applied to appropriate branches of solutions. They are not correct for another branch.…”

“…They are not correct for another branch. However, in [27] these statements have been formulated in general, without any reference to particular branches.…”

“…[27]. Since there are some subtleties, it is better to distinguish between the cases when the Kasner solution is an exact solution and an asymptotic solution.…”