Nonperturbative Continuity in Graviton Mass versus Perturbative Discontinuity

TL;DR

This paper investigates whether a small nonzero graviton mass can be consistent by examining nonperturbative solutions that show continuity in mass, contrasting with perturbative discontinuities, through a five-dimensional model and cosmological solutions.

Contribution

It demonstrates that nonperturbative solutions in a five-dimensional model are continuous in graviton mass, providing insight into the nonperturbative continuity of massive gravity theories.

Findings

Nonperturbative solutions are continuous in graviton mass.

Perturbative expansion shows discontinuity and singularities.

Helicity-zero graviton decouples as mass approaches zero.

Abstract

We address the question whether a graviton could have a small nonzero mass. The issue is subtle for two reasons: there is a discontinuity in the mass in the lowest tree-level approximation, and, moreover, the nonlinear four-dimensional theory of a massive graviton is not defined unambiguously. First, we reiterate the old argument that for the vanishing graviton mass the lowest tree-level approximation breaks down since the higher order corrections are singular in the graviton mass. However, there exist nonperturbative solutions which correspond to the summation of the singular terms and these solutions are continuous in the graviton mass. Furthermore, we study a completely nonlinear and generally covariant five-dimensional model which mimics the properties of the four-dimensional theory of massive gravity. We show that the exact solutions of the model are continuous in the mass, yet the perturbative expansion exhibits the discontinuity in the leading order and the singularities in higher orders as in the four-dimensional case. Based on exact cosmological solutions of the model we argue that the helicity-zero graviton state which is responsible for the perturbative discontinuity decouples from the matter in the limit of vanishing graviton mass in the full classical theory.