Note on massless and partially massless spin-2 particles in a curved background via a nonsymmetric tensor

H G M Fortes,D Dalmazi

doi:10.1103/physrevd.99.025013

Abstract

In the last few years we have seen an increase interest on gravitational waves due to recent and striking experimental results confirming Einstein's general relativity once more. From the field theory point of view, gravity describes the propagation of self-interacting massless spin-2 particles. They can be identified with metric perturbations about a given background metric. Since the metric is a symmetric tensor, the massless spin-2 particles present in the Einstein-Hilbert (massless Fierz-Pauli) theory are naturally described by a symmetric rank-2 tensor. However, this is not the only possible consistent massless spin-2 theory at linearized level. In particular, if we add a mass term, a new one parameter $(a_1)$ family of models ${\cal L}(a_1)$ shows up. They consistently describe massive spin-2 particles about Einstein spaces in terms of a non-symmetric rank-2 tensor. Here we investigate the massless version of ${\cal L}(a_1)$ in a curved background. In the case $a_1=-1/12$ we show that the massless spin-2 particles consistently propagate, at linearized level, in maximally symmetric spaces. A similar result is obtained otherwise $(a_1 \ne -1/12)$ where we have a non-symmetric scalar-tensor massless model. The case of partially massless non-symmetric models is also investigated.

Highlights

The recent increase in the studies on massive spin-2 particles [1,2] is partially due to the fact they can represent massive gravitons which may offer an alternative explanation for the accelerated expansion of the universe since they lead to a weaker gravitational interaction at large distances [3,4]
Lending continuity to the previous work [18] where we have studied the coupling of the new massive models Lða1Þ to curved backgrounds, in the present work we have presented the analysis of the massless versions of those models on curved spaces
In order to obtain the massless version of the Lða1Þ model coupled to a curved background, we have required the curved space versions of the corresponding flat space gauge symmetries

Summary

INTRODUCTION

The recent increase in the studies on massive spin-2 particles [1,2] is partially due to the fact they can represent massive gravitons which may offer an alternative explanation for the accelerated expansion of the universe since they lead to a weaker gravitational interaction at large distances [3,4]. That there are very low experimental upper bounds on the graviton mass, for instance from the LIGO experiment of detection of gravitational waves one has 10−22 eV, see [5,6] Another motivation is the quite recent overcome of historical theoretical obstacles in the description of massive gravitons, like the vDVZ mass discontinuity [7,8] and the existence of ghosts in the nonlinear theory [9]. Recovering previous perturbative results of [14,15] All those studies of massive spin-2 particles have considered the Fierz-Pauli (FP) theory [16] as their starting point. In [17], another family of models Lða1Þ, where a1 is an arbitrary real constant, has been suggested which describes massive spin-2 particles via a nonsymmetric rank-2 tensor eμν ≠ eνμ in flat spaces. In the present work, we seek the partially massless theories corresponding to the Lgða1Þ models

Fierz-Pauli action

PARTIALLY MASSLESS THEORIES

CONCLUSION