Revisiting the cuscuton as a Lorentz-violating gravity theory

TL;DR

This paper critically examines the cuscuton scalar field as a Lorentz-violating gravity theory, clarifying its relation to Horava gravity and Einstein-aether theory, and exploring its causal structure and applications in gravitational collapse.

Contribution

It provides a detailed analysis of the cuscuton theory's relation to other Lorentz-violating theories and investigates its causal and initial value structures.

Findings

Clarifies the relation between cuscuton, Horava gravity, and Einstein-aether theory.

Analyzes the causal structure and initial value formulation of the cuscuton theory.

Discusses the applicability of the cuscuton as a proxy for Horava gravity in gravitational collapse.

Abstract

The cuscuton is a scalar field with infinite speed of propagation. It was introduced in the context of cosmology but it has also been claimed to resemble Horava gravity in a certain limit. Here we revisit the cuscuton theory as a Lorentz-violating gravity theory. We clarify its relation with Horava gravity and Einstein-aether theory, analyze its causal structure, and consider its initial value formulation. Finally, we discuss to which extent the cuscuton theory can be used as a proxy for Horava gravity in the context of gravitational collapse and formation of universal horizons.