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

TL;DR

This paper demonstrates that in de Sitter and Anti-de Sitter spacetimes, the van Dam-Veltman-Zakharov discontinuity can be avoided by considering the relative scaling of the graviton mass and the Hubble parameter, ensuring a smooth massless limit.

Contribution

It provides a method to circumvent the vDVZ discontinuity by analyzing the interplay between graviton mass and spacetime curvature in dS_4 and AdS_4.

Findings

Smooth m->0 limit achieved when H tends to zero slower than m

Discontinuity avoided in curved spacetimes with specific scaling

Conditions for decoupling of polarization states identified

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.