The coupling of matter and spacetime geometry

Abstract

The geometrical formulation of gravity is not unique and can be set up in a variety of spacetimes. Even though the gravitational sector enjoys this freedom of different geometrical interpretations, consistent matter couplings have to be assured for a steady foundation of gravity. In generalised geometries, further ambiguities arise in the matter couplings unless the minimal coupling principle (MCP) is adopted that is compatible with the principles of relativity, universality and inertia. In this work, MCP is applied to all standard model gauge fields and matter fields in a completely general (linear) affine geometry. This is also discussed from an effective field theory perspective. It is found that the presence of torsion generically leads to theoretical problems. However, symmetric teleparallelism, wherein the affine geometry is integrable and torsion-free, is consistent with MCP. The generalised Bianchi identity is derived and shown to determine the dynamics of the connection in a unified fashion. Also, the parallel transport with respect to a teleparallel connection is shown to be free of second clock effects.

The Geometrical Trinity of Gravity

“…for the symplectic, the Wald, and the Noether currents, respectively. (For the Noether identities from (5a), see the appendix A of [24], and for the Noether identities from (5b), see the section 5.2.1 of [19]). After deriving the general expressions ( 7) and ( 9), we shall apply it to each of the cases in the "geometrical trinity" [18].…”

Teleparallel axions and cosmology

“…This assumption is made purely for simplicity, as it will not be relevant for the axion extension of the gravitational action S g we discuss here. One could also choose to couple the matter to the teleparallel spin connection, a thorough discussion of these options can for example be found in [46]. However, for the cosmological analysis we perform in Sect.…”

“…The aim of this section is to give an overview of possible axion couplings in more general teleparallel gravity theories, without studying their dynamics in detail, which would exceed the scope of this article. Further, we focus on the gravitational part of the action only, since our aim is to discuss the possible axion coupling terms; possible matter couplings to complement these actions are given in [46], and the most general contribution compatible with the cosmological symmetry is the hyperfluid discussed in [54]. In particular, in Sect.…”

Instabilities in metric-affine theories of gravity with higher order curvature terms

“…However, in the metric affine-formalism, even this prescription leads to ambiguities in several respects that lead to the appearance of terms involving the torsion and/or nonmetricity tensors (see e.g. [23,24]). For the moment, we will have in mind matter actions containing scalar fields with up to first derivatives and vector fields whose kinetic terms are gauge invariant.…”

“…Couplings to matter fields in a metric-affine framework is an interesting issue by itself, specially when it involves spinor fields (see e.g. [23,24,49]). It is not the scope of this section to carefully go through the different coupling prescriptions to matter nor their consistency.…”