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

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