Fierz-Pauli theory reloaded: from a theory of a symmetric tensor field to linearized massive gravity

TL;DR

This paper revisits the Fierz-Pauli theory of massive gravity, proposing an alternative linearized model that avoids the vDVZ discontinuity and aligns with general relativity in the massless limit.

Contribution

It introduces a new linearized massive gravity theory based on a gauge approach, resolving the vDVZ discontinuity issue present in the standard Fierz-Pauli model.

Findings

Proposes a theory with a good massless limit

Eliminates the vDVZ discontinuity problem

Maintains five degrees of freedom for the graviton

Abstract

Modifying gravity at large distances by means of a massive graviton may explain the observed acceleration of the Universe without Dark Energy. The standard paradigm for Massive Gravity is the Fierz-Pauli theory, which, nonetheless, displays well known flaws in its massless limit. The most serious one is represented by the vDVZ discontinuity, which consists in a disagreement between the massless limit of the Fierz-Pauli theory and General Relativity. Our approach is based on a field theoretical treatment of Massive Gravity: General Relativity, in the weak field approximation, is treated as a gauge theory of a symmetric rank-2 tensor field. This leads us to propose an alternative theory of linearized Massive Gravity, describing five degrees of freedom of the graviton, with a good massless limit, without vDVZ discontinuity, and depending on one mass parameter only, in agreement with the Fierz-Pauli theory.