Abstract
We construct exact non-perturbative massive solutions in the gravitational Higgs mechanism. They confirm the conclusions of arXiv:1102.4991, which are based on non-perturbative Hamiltonian analysis for the rel- evant metric degrees of freedom, that while perturbatively unitarity may not be evident, no negative norm state is present in the full nonlinear theory. The non-perturbative massive solutions do not appear to exhibit instabil- ities and describe vacuum configurations which are periodic in time, including purely longitudinal solutions with isotropic periodically expanding and contracting spatial dimensions, cosmological strings with only one peri- odically expanding and contracting spatial dimension, and also purely non-longitudinal (traceless) periodically expanding and contracting solutions with constant spatial volume. As an aside we also discuss massive solutions in New Massive Gravity. While such solutions are present in the linearized theory, we argue that already at the next-to-linear (quadratic) order in the equations of motion (and, more generally, for weak-field configurations) there are no massive solutions.
Highlights
Introduction and SummaryThe gravitational Higgs mechanism gives a non-perturbative and fully covariant definition of massive gravity [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
As an aside we discuss massive solutions in New Massive Gravity [65]. While such solutions are present in the linearized theory, we argue that already at the next-to-linear order in the equations of motion there are no massive solutions
The gravitational Higgs mechanism provides a non-perturbative definition of massive gravity in a general background
Summary
The gravitational Higgs mechanism gives a non-perturbative and fully covariant definition of massive gravity [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]. The results of [16] are in complete agreement with the full Hamiltonian analysis performed in [11] for the original model proposed by ’t Hooft [2] (see below), in which the full (gauge-fixed) Hamiltonian is explicitly positive-definite and coincides with the Hamiltonian of [16] for the relevant This holds irrespective of whether the perturbative mass term is of the Fierz-Pauli form, including in the simplest case with no higher-derivative couplings in the scalar sector, first discussed in [2].
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