Massive and mass-less Yang-Mills and gravitational fields

Abstract

Massive and mass-less Yang-Mills and gravitational fields are considered.It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the oase of gravitation, comparison of massive and mass-less theories with experiment, in particular the perihelion movement of Mercury, leads to exclusion of the massive theory. It is concluded that the graviton mass must be rigorously zero.

Can one tell Einstein's unimodular theory from Einstein's general relativity?

“…Even forgetting about the coefficients, there is a mismatch of 3/2 in the term tr T 1 T 2 ; this is the famous van Dam-Veltman discontinuity ( [17]), which indicates that there is some sort of non smoothness in the massless limit.…”

The Vainshtein mechanism in the cosmic web

“…Massive gravitons have five polarisations instead of the two in GR, and the helicity-0 mode mediates the fifth force. In a linear approximation, this helicity-0 mode does not decouple in the massless limit, leading to the so-called van Dam-Veltman-Zakharov discontinuity [4,5]. This problem can be solved by the Vainshtein mechanism.…”

Nonlinear stability of cosmological solutions in massive gravity

“…If the theory is extended to allow for a general fiducial metric 1 , expanding universe solutions can be realized in the normal branch [15][16][17], but the Higuchi bound [12] cannot be respected; for instance, for de Sitter reference metric, the scalar graviton becomes a ghost at expansion rates higher than the graviton mass [16]. 2 In the presence of a negative spatial curvature [21] or a general reference metric [15], there exists a second branch of solutions, dubbed the "self-accelerating branch", which stems from the factorized form of the temporal Stückelberg equation of motion (or equivalently, from the Bianchi identities). With the strict Friedmann-Lemaître-RobertsonWalker (FLRW) symmetry, this branch is disconnected from the normal branch and as a result, the dynamics of perturbations are dramatically different; even though the massive theories should have five degrees of freedom after the removal of the Boulware-Deser degree, only two degrees (the two tensor modes in the standard SO(3) decomposition) propagate at the linear level [15].…”

“…The massive extension of GR at the linearized level was first considered by Fierz and Pauli [1] in 1939. It was then pointed out in 1970 that the linear theory suffers from a discontinuity [2,3] in the massless limit, now known as the vDVZ discontinuity. The discontinuity can be alleviated by allowing for nonlinear termsà la Vainshtein [4] but, as pointed out in 1972 by Boulware and Deser [5], generic nonlinear massive theories contain an unwanted sixth degree, in addition to the five polarizations of massive spin-2 field, which leads to ghost instability.…”