Homogeneous and isotropic cosmology in general teleparallel gravity

TL;DR

This paper derives the most general homogeneous and isotropic teleparallel geometries, explores five connection solution branches, and analyzes their implications for cosmological dynamics in various teleparallel gravity theories.

Contribution

It provides a comprehensive classification of teleparallel geometries and their cosmological solutions, including new scalar degrees of freedom in some subclasses.

Findings

Five connection solution branches identified

Cosmological dynamics often reduce to metric or symmetric teleparallel gravity

Up to two new scalar degrees of freedom can influence cosmology

Abstract

We derive the most general homogeneous and isotropic teleparallel geometries, defined by a metric and a flat, affine connection. We find that there are five branches of connection solutions, which are connected via several limits, and can further be restricted to the torsion-free and metric-compatible cases. We apply our results to several classes of general teleparallel gravity theories and derive their cosmological dynamics for all five branches. Our results show that for large subclasses of these theories the dynamics reduce to that of closely related metric or symmetric teleparallel gravity theories, while for other subclasses up to two new scalar degrees of freedom participate in the cosmological dynamics.