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

Modifying gravity at large distances by means of a massive graviton may explain the observed acceler- ation 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 mass- less 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 Rela- tivity. 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 the- ory 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.