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.
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.
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