Fully Covariant Van Dam-Veltman-Zakharov Discontinuity, and Absence Thereof

TL;DR

This paper investigates the vDVZ discontinuity in massive gravity, demonstrating that it persists in covariant linearized theories but disappears in fully covariant non-linear models like DGP, clarifying the nature of the discontinuity.

Contribution

The paper provides explicit covariant formulations showing the persistence of the vDVZ discontinuity in linearized theories and its absence in fully covariant non-linear models such as DGP.

Findings

vDVZ discontinuity persists in covariant linearized theories

Discontinuity disappears in fully covariant non-linear models

DGP model exemplifies the absence of the discontinuity in full theory

Abstract

In both old and recent literature, it has been argued that the celebrated van Dam-Veltman-Zakharov (vDVZ) discontinuity of massive gravity is an artifact due to linearization of the true equations of motion. In this letter, we investigate that claim. First, we exhibit an explicit -albeit somewhat arbitrary- fully covariant set of equations of motion that, upon linearization, reduce to the standard Pauli-Fierz equations. We show that the vDVZ discontinuity still persists in that non-linear, covariant theory. Then, we restrict our attention to a particular system that consistently incorporates massive gravity: the Dvali-Gabadadze-Porrati (DGP) model. DGP is fully covariant and does not share the arbitrariness and imperfections of our previous covariantization, and its linearization exhibits a vDVZ discontinuity. Nevertheless, we explicitly show that the discontinuity does disappear in the fully covariant theory, and we explain the reason for this phenomenon.