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.
Highlights
MotivationsIt is an observational fact that the Universe is expanding at an accelerated rate [1,2]
We review the FP theory and the problems related to its massless limit which motivate this work, and we remark that, curiously, the original 1939 paper by Fierz and Pauli does not exactly describe what is generally known as the FP theory
In this paper we presented a gauge field theory of a massive symmetric tensor field describing a massive spin-2 particle
Summary
It is an observational fact that the Universe is expanding at an accelerated rate [1,2]. By means of a Yukawa-like potential, the gravitational effect of the vacuum energy density is exponentially suppressed at large scales, explaining the disagreement between the quantum field theory calculation and the observed cosmological value. This exponential suppression of longrange gravitational interactions is constrained by experimental evidence and, the mass of the graviton is subject to restrictive upper limits. In gauge field theory this is achieved by gauge fixing the action This procedure (gauge fixing the massless action first, adding a breaking mass term after) leads to a gauge theory of LMG describing five DOF for the massive graviton, with a good massless limit and without the vDVZ discontinuity. Page 3 of 11 171 theory of LMG should display a good massless limit since the phenomenological limits on the mass of the graviton are such that the mass term must be seen as a small perturbation of massless LG and, equivalently, as a small breaking of diffeomorphism invariance
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