Cuscuton: A Causal Field Theory with an Infinite Speed of Sound

TL;DR

The paper introduces Cuscuton, a scalar field model with infinite sound speed that remains causal despite superluminal perturbations, and explores its unique properties and potential cosmological applications.

Contribution

It presents the Cuscuton model as a novel scalar field theory with infinite sound speed, demonstrating its causality, solutions, and relevance to cosmology.

Findings

Perturbations propagate superluminally but are causally consistent.

Constant field hypersurfaces are Constant Mean Curvature surfaces.

The Cuscuton action models continuum limits of discrete fields and is quantum correction protected.

Abstract

We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a non-canonical kinetic term (or k-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces are the family of Constant Mean Curvature (CMC) hypersurfaces, which are the analogs of soap films (or soap bubbles) in a Euclidian space. This enables us to find the most general solution in 1+1 dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski spacetime, a companion paper (astro-ph/0702002) examines cosmology with Cuscuton dark energy.