Towards a High Energy Theory for the Higgs Phase of Gravity

TL;DR

This paper explores the theoretical conditions under which spontaneous Lorentz violation can occur in scalar field models relevant to dark energy and gravity, proposing a model that could serve as a high-energy completion for the Higgs phase of gravity.

Contribution

It demonstrates that standard kinetic scalar models cannot produce spontaneous Lorentz violation classically, but a large N fermion-scalar model can generate the necessary effective action.

Findings

Standard scalar models lack the features for Lorentz violation asymptotically.

A large N fermion-scalar model can produce the desired effective action.

The proposed model offers progress towards a high energy theory for the Higgs phase of gravity.

Abstract

Spontaneous Lorentz violation due to a time-dependent expectation value for a massless scalar has been suggested as a method for dynamically generating dark energy. A natural candidate for the scalar is a Goldstone boson arising from the spontaneous breaking of a U(1) symmetry. We investigate the low-energy effective action for such a Goldstone boson in a general class of models involving only scalars, proving that if the scalars have standard kinetic terms then at the {\em classical} level the effective action does not have the required features for spontaneous Lorentz violation to occur asymptotically $(t \to \infty)$ in an expanding FRW universe. Then we study the large $N$ limit of a renormalizable field theory with a complex scalar coupled to massive fermions. In this model an effective action for the Goldstone boson with the properties required for spontaneous Lorentz violation can be generated. Although the model has shortcomings, we feel it represents progress towards finding a high energy completion for the Higgs phase of gravity.