Teleparallel axions and cosmology

TL;DR

This paper introduces teleparallel axions, pseudo-scalar fields coupled to teleparallel gravity, and explores their impact on early universe cosmology, including modifications to cosmological dynamics and fixed points.

Contribution

It develops the most general teleparallel gravity theory with axion couplings and analyzes their effects on cosmological equations and dynamics.

Findings

Axion coupling affects early universe cosmology.

Presence of axial torsion influences cosmological fixed points.

Canonical coupling of pseudo-scalar to general relativity is possible.

Abstract

We consider the most general teleparallel theory of gravity whose action is a linear combination of the five scalar invariants which are quadratic in the torsion tensor. Since two of these invariants possess odd parity, they naturally allow for a coupling to pseudo-scalar fields, thus yielding a Lagrangian which is even under parity transformations. In analogy to similar fields in gauge theories, we call these pseudo-scalar fields \emph{teleparallel axions}. For the most general coupling of a single axion field, we derive the cosmological field equations. We find that for a family of cosmologically symmetric teleparallel geometries, which possess non-vanishing axial torsion, the axion coupling contributes to the cosmological dynamics in the early universe. Most remarkably, this contribution is also present when the axion is coupled to the teleparallel equivalent of general relativity, hence allowing for a canonical coupling of a pseudo-scalar to general relativity. For this case we schematically present the influence of the axion coupling on the fixed points in the cosmological dynamics understood as dynamical system. Finally, we display possible generalizations and similar extensions in other geometric frameworks to model gravity.