Caustic avoidance in Horava-Lifshitz gravity

TL;DR

This paper investigates caustic formation in a specific version of Horava-Lifshitz gravity, showing that under certain conditions, caustics do not form, supporting the theory's consistency and implications for dark matter models.

Contribution

It demonstrates the absence of caustics in a version of Horava-Lifshitz gravity with specific conditions, extending understanding of the theory's stability and physical implications.

Findings

No caustic formation with plane symmetry if λ≠1.

Caustics cannot form without matter source under the given conditions.

Higher codimension caustics are prevented by nonlinear higher curvature effects.

Abstract

There are at least four versions of Horava-Lishitz gravity in the literature. We consider the version without the detailed balance condition with the projectability condition and address one aspect of the theory: avoidance of caustics for constant time hypersurfaces. We show that there is no caustic with plane symmetry in the absence of matter source if \lambda\ne 1. If \lambda=1 is a stable IR fixed point of the renormalization group flow then \lambda is expected to deviate from 1 near would-be caustics, where the extrinsic curvature increases and high-energy corrections become important. Therefore, the absence of caustics with \lambda\ne 1 implies that caustics cannot form with this symmetry in the absence of matter source. We argue that inclusion of matter source will not change the conclusion. We also argue that caustics with codimension higher than one will not form because of repulsive gravity generated by nonlinear higher curvature terms. These arguments support our conjecture that there is no caustic for constant time hypersurfaces. Finally, we discuss implications to the recently proposed scenario of ``dark matter as integration constant''.