Self-Protection of Massive Cosmological Gravitons

TL;DR

This work analyzes the stability of a cosmological graviton with a leading infrared deformation—the Fierz–Pauli mass term—on general Friedman backgrounds. By employing the Goldstone–Stückelberg formalism, the authors derive a scalar sector with time-dependent kinetic coefficients that determine unitarity and classical stability, yielding bounds $m^2>H^2$ in de Sitter and $m^2>H^2+\u0307{\dot{H}}$ (unitarity) and $m^2>H^2+dot{H}/3$ (classical) for generic Friedman spacetimes. They show that as the Universe evolves backward in time the system enters a strong-coupling regime before any unitarity violation, hence a self-protection mechanism preserves a healthy theory for expanding histories and constrains nonlinear completion. The results imply that massive cosmological gravitons can be viable in realistic cosmologies, with de Sitter as a boundary case and matter couplings leaving the bounds robust. The study also discusses potential nonlinear completions and ghost-related issues (Boulware–Deser) in deformations of gravity.

Abstract

Relevant deformations of gravity present an exciting window of opportunity to probe the rigidity of gravity on cosmological scales. For a single-graviton theory, the leading relevant deformation constitutes a graviton mass term. In this paper, we investigate the classical and quantum stability of massive cosmological gravitons on generic Friedman backgrounds. For a Universe expanding towards a de Sitter epoch, we find that massive cosmological gravitons are self-protected against unitarity violations by a strong coupling phenomenon.