# Gravity with explicit spacetime symmetry breaking and the Standard-Model Extension

## TL;DR

This paper explores the use of the Standard-Model Extension framework to describe gravity theories with explicit spacetime symmetry breaking, demonstrating consistency with Bianchi identities in certain cases and analyzing specific models.

## Contribution

It extends the SME to include explicit spacetime symmetry breaking in gravity, showing it can be consistent with fundamental identities and applying it to specific gravity models.

## Key findings

- SME can describe explicit symmetry breaking in gravity with matter couplings
- Consistency with Bianchi identities is possible in many cases
- Analyzed models include ghost-free massive gravity and Horava gravity

## Abstract

The Standard-Model Extension (SME) is the general phenomenological framework used to investigate Lorentz violation at the level of effective field theory. It has been used to obtain stringent experimental bounds on Lorentz violation in a wide range of tests. In the gravity sector of the SME, it is typically assumed that the spacetime symmetry breaking occurs spontaneously in order to avoid potential conflicts with the Bianchi identities. A post-Newtonian limit as well as matter-gravity couplings in the SME have been developed and investigated based on this assumption. In this paper, the possibility of using the SME to also describe gravity theories with explicit spacetime symmetry breaking is investigated. It is found that in a wide range of cases, particularly when matter-gravity couplings are included, consistency with the Bianchi identities can be maintained, and therefore the SME can be used to search for signals of the symmetry breaking. Two examples with explicit breaking are considered. The first is ghost-free massive gravity with an effective metric that couples to matter. The second is Horava gravity coupled with matter in an infrared limit.