Massive Gravity: Resolving the Puzzles

TL;DR

This work constructs a diffeomorphism-invariant Higgs mechanism for gravity in which four scalar fields give the graviton a mass $m_g = M v^2$ via spontaneous symmetry breaking. It analyzes the full nonlinear structure, showing a five-degree-of-freedom massive graviton composed of tensor, vector, and scalar modes, and demonstrates that the vDVZ discontinuity is avoided by a Vainshtein mechanism: below a model-dependent radius $R_V$ the nonlinearities restore General Relativity, while above $R_V$ deviations persist. The authors show that the Vainshtein scale depends on the nonlinear completion of the mass term, deriving several scenarios that connect to, and in some cases generalize, the DGP results; they also discuss quantum cutoff scales that render the dangerous scalar degree of freedom harmless. Overall, the paper provides a classical and semi-quantitative framework for a ghost-free, diffeomorphism-invariant massive gravity with a controllable GR limit, and clarifies how nonlinear scalar dynamics shape observational predictions and theoretical consistency.

Abstract

We consider the massless limit of Higgs gravity, where the graviton becomes massive when the scalar fields acquire expectation values. We determine the Vainshtein scale and prove that massive gravity smoothly goes to General Relativity below this scale. We find that the Vainshtein scale depends on the particular action of scalar fields used to give mass to the graviton.