A non-local theory of massive gravity

Abstract

We construct a fully covariant theory of massive gravity which does not require the introduction of an external reference metric, and overcomes the usual problems of massive gravity theories (fatal ghosts instabilities, acausality and/or vDVZ discontinuity). The equations of motion of the theory are non-local, but respect causality. The starting point is the quadratic action proposed in the context of the degravitation idea. We show that it is possible to extended it to a fully non-linear covariant theory. This theory describes the five degrees of freedom of a massive graviton plus a scalar ghost. However, contrary to generic non-linear extensions of Fierz-Pauli massive gravity, the ghost has the same mass m as the massive graviton, independently of the background, and smoothly goes into a non-radiative degree of freedom for m-> 0. As a consequence, for $m\sim H_0$ the vacuum instability induced by the ghost is irrelevant even over cosmological time-scales. We finally show that an extension of the model degravitates a vacuum energy density of order $M_{Planck}^4$ down to a value of order $M_{Planck}^2 m^2$, which for $m \sim H_0$ is of order of the observed value of the vacuum energy density.