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.
Highlights
Lorentz symmetry appears to be a fundamental symmetry of the Standard Model of particle physics and experimental constraints are impressively tight
Horava gravity is a prototypical example of a theory with a preferred foliation and an elliptic, instantaneous mode that persists even at low energies
What makes a certain foliation preferred in this theory is that the field equations have higher order than second time derivatives in every other foliation
Summary
Lorentz symmetry appears to be a fundamental symmetry of the Standard Model of particle physics and experimental constraints are impressively tight (see e.g. [1]). Neighborhood of some event, the æther will define some preferred time direction Another Lorentz-violating theory that has attracted a lot of attention recently is Horava gravity [3]. In a covariant form the low energy limit of Horava gravity can be considered dynamically equivalent to Einstein-æther theory with the additional restriction uμ 1⁄4 − pffi−ffiffiffigffiffiμ∂ffiffiνffiμffi∂ffiTffiμffiffiTffiffiffi∂ffiffiffiνffiffiTffiffi ; ð3Þ where T is a scalar field [4]. In this formulation the level surfaces of T define the preferred foliation. To which extent the study of dynamical formation of a universal horizon in cuscuton theory in Ref. [21] can teach us something about universal horizon formation in Horava gravity hinges strongly on the relation between the two theories and their causal structure
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