Anisotropic spacetimes in $f(T,B)$ theory III: LRS Bianchi III Universe

TL;DR

This paper investigates the long-term behavior of $f(T, B)$ gravity in an anisotropic Bianchi III universe, showing that the universe tends toward an accelerated or non-accelerated isotropic state depending on the model parameters.

Contribution

It demonstrates the existence of an attractor solution in $f(T, B)$-theory that leads to either accelerated flat FLRW or non-accelerated Bianchi III geometries.

Findings

An attractor always exists for the field equations.

The attractor can be an accelerated flat FLRW universe.

The attractor can also be a non-accelerated Bianchi III universe.

Abstract

We study the asymptotic dynamics of $f(T, B)$-theory in an anisotropic Bianchi III background geometry. We show that an attractor always exists for the field equations, which depends on a free parameter provided by the specific $f(T, B)$ functional form. The attractor is an accelerated spatially flat FLRW or non-accelerated LRS Bianchi III geometry. Consequently, the $f(T, B)$-theory provides a spatially flat and isotropic accelerated Universe.