The m→0 limit for massive graviton in dS4 and AdS4 — How to circumvent the van Dam–Veltman–Zakharov discontinuity

We show that, by considering physics in dS4 or AdS4 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 dS4 or AdS4 space, tends to zero slower than the mass of the graviton m.