# Causal field theory with an infinite speed of sound

## 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 noncanonical 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 is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in 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 space-time, a companion paper examines cosmology with Cuscuton dark energy.

- Authors:

- Institute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, MS-51, 60 Garden Street, Cambridge, Massachusetts 02138 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 21020355

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.083513; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CORRECTIONS; COSMOLOGY; COUPLING; DEGREES OF FREEDOM; ENTROPY; MATHEMATICAL SOLUTIONS; MINKOWSKI SPACE; NONLUMINOUS MATTER; PHASE SPACE; QUANTUM FIELD THEORY; SCALAR FIELDS; SOUND WAVES; SPACE-TIME

### Citation Formats

```
Afshordi, Niayesh, Chung, Daniel J. H., Geshnizjani, Ghazal, and Department of Physics, University of Wisconsin, Madison, Wisconsin 53706.
```*Causal field theory with an infinite speed of sound*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.083513.

```
Afshordi, Niayesh, Chung, Daniel J. H., Geshnizjani, Ghazal, & Department of Physics, University of Wisconsin, Madison, Wisconsin 53706.
```*Causal field theory with an infinite speed of sound*. United States. doi:10.1103/PHYSREVD.75.083513.

```
Afshordi, Niayesh, Chung, Daniel J. H., Geshnizjani, Ghazal, and Department of Physics, University of Wisconsin, Madison, Wisconsin 53706. Sun .
"Causal field theory with an infinite speed of sound". United States.
doi:10.1103/PHYSREVD.75.083513.
```

```
@article{osti_21020355,
```

title = {Causal field theory with an infinite speed of sound},

author = {Afshordi, Niayesh and Chung, Daniel J. H. and Geshnizjani, Ghazal and Department of Physics, University of Wisconsin, Madison, Wisconsin 53706},

abstractNote = {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 noncanonical 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 is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in 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 space-time, a companion paper examines cosmology with Cuscuton dark energy.},

doi = {10.1103/PHYSREVD.75.083513},

journal = {Physical Review. D, Particles Fields},

number = 8,

volume = 75,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}