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

TL;DR

This work develops a comprehensive set of exact and approximate cosmological solutions in teleparallel F(T,B) gravity for TRW spacetimes. By imposing a power-law scale factor and exploring linear and non-linear EoS fluids as well as scalar-field sources, the authors obtain diverse solution classes, especially for the flat case $k=0$ where many solutions reduce to $F(T,B)=F_1(T)+F_2(B)$ forms. For non-flat geometries ($k=\pm1$), solutions exist only in particular subcases, underscoring the increased mathematical complexity of these spacetimes. The results illuminate how F(T,B) gravity can accommodate dark-energy phenomenology such as quintessence and phantom behavior, including the potential to model cosmological bounce scenarios, and lay groundwork for future observational data fitting. Overall, the paper significantly broadens the catalog of analytic teleparallel cosmologies and highlights the role of the boundary term $B$ in shaping cosmic evolution.

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.