Completing Lorentz violating massive gravity at high energies
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ompleting Lorentz Violating Massive Gravity at High Energies1 D. Blasa and S. Sibiryakova,b,c,* a
CERN Theory Division, Geneva 23, CH1211 Switzerland Institut de Théorie des Phénoménes Physiques, EPFL, Lausanne, CH1015 Switzerland c Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, 117312 Russia *email: [email protected] b
Received November 11, 2014
Abstract—Theories with massive gravitons are interesting for a variety of physical applications, ranging from cosmological phenomena to holographic modeling of condensed matter systems. To date, they have been for mulated as effective field theories with a cutoff proportional to a positive power of the graviton mass mg and much smaller than that of the massless theory (MP ≈ 1019 GeV in the case of general relativity). In this paper, we present an ultraviolet completion for massive gravity valid up to a high energy scale independent of the graviton mass. The construction is based on the existence of a preferred time foliation combined with spon taneous condensation of vector fields. The perturbations of these fields are massive and below their mass, the theory reduces to a model of Lorentz violating massive gravity. The latter theory possesses instantaneous modes whose consistent quantization we discuss in detail. We briefly study some modifications to gravita tional phenomenology at lowenergies. The homogeneous cosmological solutions are the same as in the stan dard cosmology. The gravitational potential of point sources agrees with the Newtonian one at distances small –1
with respect to m g . Interestingly, it becomes repulsive at larger distances. Contribution for the JETP special issue in honor of V.A.Rubakov’s 60th birthday DOI: 10.1134/S1063776115030164 1
1. INTRODUCTION
Can gravity be mediated by a massive tensor field? This straightforward question has generated a lot of controversy since it was first formulated by Fierz and Pauli [1]. The situation is remarkably different from the case of gauge interactions mediated by vector fields, where the Higgs mechanism provides a clear cut way to give mass to the vector bosons within a weakly coupled theory. The differences fall into two categories. First, a generic Lorentz invariant theory with massive spin2 fields (gravitons) presents instabil ities in the sector of additional polarizations appearing in the massive, as opposed to massless case—the “Goldstone” sector. These instabilities arise around realistic backgrounds and endanger the consistency of the theory even at low energies [2, 3]. It was first real ized by Rubakov [4] that these problems can be avoided by breaking the Lorentz invariance. This approach has lead to the formulation of a class of Lorentz violating (LV) massive gravities as consistent effective field theories (EFTs) [5] (see [6] for review). An alternative way to improve the behavior of the Goldstone sector while preserving the Lorentz invari ance has been found in [7] and consists in a judicious
choice of the couplings for the interactions of the
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