Regular Article – Theoretical Physics
Fierz–Pauli theory reloaded: from a theory of a symmetric tensor field to linearized massive gravity
Rudolf Peierls Centre for Theoretical Physics, Oxford University, Oxford, UK
2 Dipartimento di Fisica, Università di Genova, Genoa, Italy
3 Istituto Nazionale di Fisica Nucleare-Sezione di Genova, Genoa, Italy
Accepted: 5 February 2021
Published online: 19 February 2021
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.
© The Author(s) 2021
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