Anisotropic spacetimes in $f(T,B)$ theory II: Kantowski-Sachs Universe

TL;DR

This paper explores anisotropic Kantowski-Sachs cosmologies within the $f(T,B)$ gravity framework, deriving exact solutions and analyzing their stability, revealing conditions under which the universe evolves towards isotropy with zero spatial curvature.

Contribution

It provides new exact solutions and stability analysis for anisotropic Kantowski-Sachs universes in $f(T,B)$ gravity, highlighting conditions for isotropization.

Findings

Isotropic universe acts as an attractor in certain $f(T,B)$ models.

No future attractors with nonzero spatial curvature.

Exact solutions for the evolution of anisotropic cosmologies.

Abstract

In the context of the modified teleparallel $f(T, B)$-theory of gravity, we consider a homogeneous and anisotropic background geometry described by the Kantowski-Sachs line element. We derive the field equations and investigate the existence of exact solutions. Furthermore, the evolution of the trajectories for the field equations is studied by deriving the stationary points at the finite and infinite regimes. For the $f(T,B)=T+F\left( B\right) $ theory, we prove that for a specific limit of the function $F\left( B\right) $, the anisotropic Universe has the expanding and isotropic Universe as an attractor with zero spatial curvature. We remark that there are no future attractors where the asymptotic solution describes a Universe with nonzero spatial curvature.