Massive gravity from Dirichlet boundary conditions

TL;DR

This work presents a five-dimensional framework where a spurious extra dimension with mixed boundary conditions yields four-dimensional massive gravity on a brane. At linear order it reproduces Fierz-Pauli gravity and, via a helicity-0 mode, exhibits Vainshtein screening; the decoupling limit and the role of extrinsic-curvature terms determine the presence of ghosts and the strong-coupling scales. The model admits flat brane solutions with tension and discusses both hard and soft mass realizations, including a fully five-dimensional diffeomorphism-invariant appendix that can yield a ghost-free soft mass. Together, these results offer a geometrical, boundary-condition-based approach to non-linear massive gravity and degravitation, highlighting both stability concerns and avenues for cosmological applications.

Abstract

We propose an explicit non-linear realization of massive gravity, which relies on the introduction of a spurious compact extra dimension, on which we impose half-Newmann and half-Dirichlet boundary conditions. At the linearized level, we recover the expected gravitational exchange amplitude between two sources mediated by a massive Fierz-Pauli spin-2 field, while cubic interactions in the additional helicity-0 mode give rise to the expected Vainsthein mechanism. We also show that this framework can accommodate for a flat four-dimensional geometry in the presence of a cosmological constant, putting this framework on a good footing for the study of degravitation.