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 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.
Highlights
Besides the most well-known formulation of general relativity in terms of curvature, alternative formulations based on torsion or nonmetricity have been conceived [16], giving rise to the so called symmetric teleparallel equivalent of general relativity (STEGR) [17] and the teleparallel equivalent of general relativity (TEGR) [18,19,20]
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
We study the cosmological dynamics of the teleparallel axion model, whose action and field equations we displayed in the preceding section
Summary
Besides the most well-known formulation of general relativity in terms of curvature, alternative formulations based on torsion or nonmetricity have been conceived [16], giving rise to the so called symmetric teleparallel equivalent of general relativity (STEGR) [17] and the teleparallel equivalent of general relativity (TEGR) [18,19,20]. Modifying teleparallel theories of gravity with additional non-minimally coupled scalar fields has been studied throughout the literature [31,32,33,34,35,36,37,38], and we will extend this class in this article by considering a non-minimal coupling to a pseudo-scalar field. A interesting subclass emerges when we reduce the part of the action constructed from the three parity-even torsion invariants to TEGR In this way the teleparallel torsion based formulation of general relativity allows for a natural coupling of pseudo-scalars. Both for the general theory and the special case of the axion coupling to TEGR, we study the cosmological dynamics.
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