Linear gravity in de Sitter universe

We give in this paper an explicit construction of the covariant quantization of the rank-2 “massless” tensor field on de Sitter (dS) space (linear covariant quantum gravity on a dS background). The main ingredient of the construction is an indecomposable representation of de Sitter group with different indecomposability channels. We here make the choice of a specific gauge fixing in order to get the simplest possible structure of the involved Gupta-Bleuler trip- lets. We describe the related Krein space structure and covariant field operators ??????. We show that our gauge fixing eliminates any infrared divergence in the two-point function for the traceless part of this field. But it is not possible to do the same for the pure trace part (conformal sector). This work is in the continuation of our previous ones concerning the “minimally coupled scalar fields and the “massive” tensor field on dS.