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.

arXiv comment20 pages, 5 figures;fixed typos and added references

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Cited by in corpus (9)

• Starting the Universe: Stable Violation of the Null Energy Condition and Non-standard Cosmologies
• Accelerating Universe and Cosmological Perturbation in the Ghost Condensate
• Ghost condensate and generalized second law
• Dynamical system analysis of cosmological evolution in the Aether scalar tensor theory
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• Ghost Condensate Busting
• Lorentz Violation and Superpartner Masses
• Ghost Dark Matter
• Regulator Dependence of the Proposed UV Completion of the Ghost Condensate