Stability of Massive Cosmological Gravitons

TL;DR

The paper proves a sharp stability/unitarity boundary for massive spin-2 fields in (A)dS backgrounds: the theory is stable only when $m^2\ge 2\Lambda/3$, with instability from helicity-0 contributions when $m^2<2\Lambda/3$. At the critical line $m^2=2\Lambda/3$ the theory becomes partially massless, possessing four propagating degrees of freedom with helicities $(\pm2,\pm1)$ and an emergent scalar gauge invariance that removes helicity-0. A 3+1 Hamiltonian analysis shows that, for $m^2>2\Lambda/3$, all five helicities propagate in a unitary, positive-energy fashion inside the de Sitter horizon; for $m^2<2\Lambda/3$ the helicity-0 sector carries negative energy, signaling instability. These results map a clear phase diagram in the $(m^2,\Lambda)$ plane and connect unitarity, energy positivity, and causality for massive gravitons in cosmological spacetimes, with extensions to higher spins and implications for partially massless theories.

Abstract

We analyze the physics of massive spin 2 fields in (A)dS backgrounds and exhibit that: The theory is stable only for masses m^2 >= 2Λ/3, where the conserved energy associated with the background timelike Killing vector is positive, while the instability for m^2<2Λ/3 is traceable to the helicity 0 energy. The stable, unitary, partially massless theory at m^2=2Λ/3 describes 4 propagating degrees of freedom, corresponding to helicities (+/-2,+/-1) but contains no 0 helicity excitation.