Cosmological solutions in teleparallel $F(T,B)$ gravity

TL;DR

This paper derives new exact and approximate solutions in teleparallel $F(T,B)$ gravity for various cosmological models, including perfect fluids and scalar fields, with implications for dark energy and cosmic acceleration.

Contribution

It introduces novel $F(T,B)$ solutions for flat and non-flat Robertson--Walker cosmologies, expanding the understanding of teleparallel gravity's role in cosmology.

Findings

Found new solutions for linear and non-linear perfect fluids.

Derived solutions for scalar field cosmologies with power-law and exponential forms.

Identified specific cases where solutions apply to flat and curved universes.

Abstract

In this paper, we find several teleparallel $F(T,B)$ solutions for a Robertson--Walker (TRW) cosmological spacetime. We first set and solve the $F(T,B)$-type field equations for a linear perfect fluid. Using similar techniques, we then find new $F(T,B)$ solutions for non-linear perfect fluids with a weak quadratic correction term to the linear equation of state (EoS). Finally, we solve for new classes of $F(T,B)$ solutions for a scalar field source by assuming a power-law scalar field and then an exponential scalar field in terms of the time coordinate. For flat cosmological cases ($k=0$ cases), we find new exact and approximate $F(T,B)$ solutions. For non-flat cases ($k=\pm 1$ cases), we only find new teleparallel $F(T,B)$ solutions for some specific and well-defined cosmological expansion subcases. We conclude by briefly discussing the impact of these new teleparallel solutions on cosmological processes such as dark energy (DE) quintessence and phantom energy models.