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

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.

11 pages, 7 figures, v3: some new results added, v4: some clarifications added

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Cited by in corpus (14)

• Teleparallel Gravity: From Theory to Cosmology
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Covariant formulation of scalar-torsion gravity
• Quest for the extra degree of freedom in f(T) gravity
• Noether Symmetries and Quantum Cosmology in Extended Teleparallel Gravity
• Kasner cosmology in bumblebee gravity
• Dynamical properties of Bianchi-I spacetimes in $f(R)$ gravity
• Anisotropic cosmological dynamics in $f(T)$ gravity in the presence of a perfect fluid
• Bianchi I cosmological solutions in teleparallel gravity
• Bianchi Type Cosmological Models in $f(T)$ Tele-parallel Gravity
• Spatially Homogeneous Teleparallel Gravity: Bianchi I
• A generic dynamical system formulation for Bianchi-I cosmology with isotropic fluid in $f(Q)$ gravity
• Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions
• More on Bianchi I spacetimes and f(T) gravity