The m->0 limit for massive graviton in dS_4 and AdS_4. How to circumvent the van Dam-Veltman-Zakharov discontinuity

TL;DR

Problem addressed: the van Dam-Veltman-Zakharov discontinuity questions whether extra polarizations of a massive graviton decouple in the massless limit. Approach: study the graviton propagator in $dS_4$ and $AdS_4$ for arbitrary $m$ and horizon scale $H$, derive the massless and massive propagator components $G^0,E^0$ and $G^m,E^m$ as functions of the invariant $u$, and study the $m/H$ dependence. Findings: the $m \to 0$ limit is smooth when $m/H \to 0$, so the extra polarizations decouple and one recovers the massless propagator; when $m/H \to \infty$ the flat-space VZ result is restored; for finite but small $m/H$ the extra polarizations couple weakly, modifying gravity at all scales but with the horizon shielding extreme long-distance effects. Significance: demonstrates a mechanism to realize viable gravity with tiny massive gravitons in curved backgrounds, with observationally testable consequences and horizon-scale phenomenology.

Abstract

We show that, by considering physics in dS_4 or AdS_4 spacetime, one can circumvent the van Dam - Veltman - Zakharov theorem which requires that the extra polarization states of a massive graviton do not decouple in the massless limit. It is shown that the smoothness of the m->0 limit is ensured if the H (``Hubble'') parameter, associated with the horizon of the dS_4 or AdS_4 space, tends to zero slower than the mass of the graviton m.