  We give in this paper an explicit construction of the covariant quantization
of the rank-two massless tensor field on de Sitter space (linear covariant
quantum gravity on a de Sitter background). The main ingredient of the
construction is an indecomposable representation of de Sitter group. We here
make the choice of a specific simple gauge fixing. 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). We describe the related Krein space
structure and covariant field operators. This work is in the continuation of
our previous ones concerning the massless minimally coupled scalar fields and
the massive tensor field on de Sitter.
