Reduced geometry and its role in explicit spacetime symmetry violation

TL;DR

This paper explores methods to reconcile explicit spacetime symmetry violation with Riemannian geometry in gravity, proposing that isometries can help determine compatible SME background fields, demonstrated in cosmological models.

Contribution

It introduces a new technique based on isometries to address explicit spacetime symmetry violation within Riemannian geometry in gravity.

Findings

Isometries of a gravitational system can determine compatible SME backgrounds.

The proposed method works for cosmological time evolution with SME backgrounds.

A third technique based on isometries is introduced and demonstrated.

Abstract

The incompatibility of explicit diffeomorphism violation with Riemannian geometry within the gravitational Standard-Model Extension (SME) is revisited. We review two methods of how to deal with this problem. The first is based on an approach proposed originally by St\"{u}ckelberg and the latter is to restrict spacetime geometry via the dynamical field equations and the second Bianchi identities. Moreover, a third technique is introduced in this work, which relies on isometries of a gravitational system. Our conclusion is that an SME background field configuration compatible with Riemannian geometry is more likely to be determined the more diffeomorphisms are isometries of the particular system. The proposal is demonstrated to work for cosmological time evolution with the SME backgrounds $u$ and $s^{\mu\nu}$ present. This finding has the potential to provide an alternative treatment of explicit spacetime symmetry violation in gravity.