Sigma-Model Aether

TL;DR

This paper explores the properties and constraints of a Lorentz-violating vector field theory with a sigma-model kinetic term, analyzing mode propagation, experimental bounds, and cosmological evolution including extra dimensions.

Contribution

It provides a detailed phenomenological analysis of a Lorentz-violating aether model with a sigma-model kinetic term, including stability conditions, mode analysis, and cosmological implications.

Findings

Unique curvature coupling avoids superluminal modes.

Experimental bounds constrain the parameter space.

Aether naturally aligns orthogonal to constant-density surfaces in FRW cosmology.

Abstract

Theories of low-energy Lorentz violation by a fixed-norm "aether" vector field with two-derivative kinetic terms have a globally bounded Hamiltonian and are perturbatively stable only if the vector is timelike and the kinetic term in the action takes the form of a sigma model. Here we investigate the phenomenological properties of this theory. We first consider the propagation of modes in the presence of gravity, and show that there is a unique choice of curvature coupling that leads to a theory without superluminal modes. Experimental constraints on this theory come from a number of sources, and we examine bounds in a two-dimensional parameter space. We then consider the cosmological evolution of the aether, arguing that the vector will naturally evolve to be orthogonal to constant-density hypersurfaces in a Friedmann-Robertson-Walker cosmology. Finally, we examine cosmological evolution in the presence of an extra compact dimension of space, concluding that a vector can maintain a constant projection along the extra dimension in an expanding universe only when the expansion is exponential.