‘Hidden’ symmetry of linearized gravity in de Sitter space

Abstract

We demonstrate that the linearized Einstein gravity in de Sitter (dS) spacetime besides the evident symmetries also possesses the additional (local) symmetry hµν → hµν + Eµν χ, where Eµν is a spintwo projector tensor and χ is an arbitrary constant function. We argue that an anomalous symmetry associated with this hitherto 'hidden' property of the existing physics is indeed at the origin of 'dS breaking' in linearized quantum gravity.

Massive Rarita-Schwinger field in de Sitter space

“…Furthermore, knowledge of the dS massive fields enables us to display the structure of the field theory that appears at the massless limit. Massless field theories in dS spacetime possess some peculiarities that have no analog in flat case (see for instance [16,33,34]). Having an expression for the dS massive fields permits one to determine the indecomposable representation describing the dS massless fields.…”

Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime

“…In a recent work [1], with respect to a coordinateindependent approach based on ambient space notations, we have shown that linearized quantum gravity in dS spacetime, constructed through canonical quantization and the usual representation of the canonical commutation relations, suffers from a hitherto 'hidden' local (gauge-like) anomaly. More technically, we have shown that the classical theory besides the spacetime symmetries generated by the Killing vectors and the evident gauge symmetry, 1…”

“…in which E µν and χ, respectively, stand for a second-order differential operator (a spin-two projector tensor) and an arbitrary constant function [1]. This hitherto 'hidden' gauge-like symmetry, however, becomes anomalous x = (x 0 = H −1 tan ρ, (H cos ρ) −1 u), ρ ∈] −π 2 , π 2 [, u ∈ S 3 , in which, the graviton field hµν can be expressed in terms of the second-rank symmetric tensor spherical harmonics on the threespheres.…”

“…It contains two different types of non-physical modes which are indeed the price to pay for the fully covariance of the theory. The first one appears due to the evident gauge symmetry (1) and is similar to the non-physical states in gauge quantum field theories in Minkowski space, while the other appears due to the presence of the gauge-like symmetry (2) and is similar to the case of dS minimally coupled scalar field [11][12][13]. [The latter with negative frequency, as already pointed out, is responsible for dS breaking in linearized quantum gravity with respect to the canonical quantization and the usual representation of the canonical commutation relations.]…”

“…In Section V, providing a new representation of the canonical commutation relations, the graviton quantum field is given. It is causal and it is covariant in the usual strong sense: (1,4), while U stands for the corresponding indecomposable representation of the dS group on the space of states. This implies that the field is defined on the whole dS spacetime.…”