# Testing Lorentz invariance of dark matter with satellite galaxies

## TL;DR

This paper proposes a framework to test Lorentz invariance in dark matter by analyzing satellite galaxy dynamics, identifying observable signatures that could constrain Lorentz-violating theories with future data.

## Contribution

It introduces a numerical model for satellite galaxy dynamics under Lorentz violation, highlighting observable signatures for testing dark matter Lorentz invariance.

## Key findings

- LV forces affect satellite internal dynamics
- Observable signatures include changes in velocity dispersion and mass profiles
- Framework enables future constraints on LV parameters in dark matter

## Abstract

We develop the framework for testing Lorentz invariance in the dark matter sector using galactic dynamics. We consider a Lorentz violating (LV) vector field acting on the dark matter component of a satellite galaxy orbiting in a host halo. We introduce a numerical model for the dynamics of satellites in a galactic halo and for a galaxy in a rich cluster to explore observational consequences of such an LV field. The orbital motion of a satellite excites a time dependent LV force which greatly affects its internal dynamics. Our analysis points out key observational signatures which serve as probes of LV forces. These include modifications to the line of sight velocity dispersion, mass profiles and shapes of satellites. With future data and a more detailed modeling these signatures can be exploited to constrain a new region of the parameter space describing the LV in the dark matter sector.