On Kasner solution in Bianchi I $f(T)$ cosmology

TL;DR

This paper investigates the properties of Kasner solutions in $f(T)$ cosmology, clarifying contradictions in previous studies and analyzing their stability and asymptotic behavior in different branches of the theory.

Contribution

It provides a detailed comparison of vacuum solutions in $f(T)$ and $f(R)$ gravity, clarifies the nature of Kasner solutions, and explores their stability and attractor properties.

Findings

Kasner solution is an exact solution for the $T=0$ branch.

Kasner solution is an asymptotic solution for $T e 0$ branch.

Kasner solution acts as a past attractor for $T<0$ and an attractor for both past and future when $T>0$.

Abstract

Recently cosmological dynamics of anisotropic Universe in $f(T)$ gravity became an area of intense investigations. Some earlier papers devoted to this issue contain contradictory claims about the nature and propertied of vacuum solutions in this theory. The goal of the present paper is to clarify this situation. We compare properties of $f(T)$ and $f(R)$ vacuum solutions and outline differences between them. The Kasner solution appears to be an exact solution for the $T=0$ branch, and an asymptotic solution for $T \ne 0$ branch. It is shown that Kasner solution is the past attractor if $T<0$, being past and future attractor for $T>0$ branch.