# Unimodular gravity theory with external sources in a Lorentz-symmetry breaking scenario

## TL;DR

This paper investigates how Lorentz symmetry breaking via a Chern-Simons term affects interactions in linearized unimodular gravity, revealing subtle differences from standard theories that are experimentally indistinguishable at leading order.

## Contribution

It introduces a perturbative analysis of Lorentz symmetry breaking effects in unimodular gravity with external sources, highlighting the qualitative similarities and subtle differences from standard WTDIFF theory.

## Key findings

- Lorentz violation causes numerical differences in source interactions.
- Results are qualitatively similar to standard WTDIFF theory.
- Differences become indistinguishable at leading order in perturbation.

## Abstract

This paper is dedicated to the study of interactions between stationary field sources for the linearized unimodular gravity or WTDIFF theory in a model which exhibits Lorentz symmetry breaking due to the presence of the linearized topological Chern-Simons term in $3 + 1$ dimensions, where the Lorentz symmetry breaking is caused by a single background vector $v^{\mu}$. Since the background vector is very tiny, we treat it perturbatively up to second order and we focus on physical phenomena which have no counterpart in standard WTDIFF theory. We consider effects related to field sources describing point-like particles and cosmic strings. We show that in a Lorentz violating scenario the interaction between external sources lead to numerically different results for linerarized Eintein-Hilbert (LEH) and WTDIFF theories, however both results are qualitatively similar and can be equalized after a rescaling of the Lorentz breaking source term which makes an experimental distinction impossible at leading order in pertubation theory as far as point particles and cosmic strings are concerned.