# Notes on Matter in Horava-Lifshitz Gravity

## TL;DR

This paper examines scalar and dust dynamics in Horava-Lifshitz gravity, revealing superluminal propagation issues and showing dust avoids singularity formation, thus impacting the theory's predictability.

## Contribution

It provides an analysis of matter behavior in Horava-Lifshitz gravity, highlighting causality constraints and the non-collapse of dust without singularities.

## Key findings

- Scalar field can propagate superluminally without an upper speed limit.
- Causality constraints restrict the form of the scalar action.
- Dust does not form singularities but re-expands after reaching maximum density.

## Abstract

We investigate the dynamics of a scalar field governed by the Lifshitz-type action which should appear naturally in Horava-Lifshitz gravity. The wave of the scalar field may propagate with any speed without an upper bound. To preserve the causality, the action cannot have a generic form. Due to the superluminal propagation, a formation of a singularity may cause the breakdown of the predictability of the theory. To check whether such a catastrophe could occur in Horava-Lifshitz gravity, we investigate the dynamics of a dust. It turns out that the dust does not collapse completely to form a singularity in a generic situation, but expands again after it attains a maximum energy density.