Non-perturbative Massive Solutions in Gravitational Higgs Mechanism

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 relevant 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 instabilities 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 periodically 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.