Physical equivalence between the covariant and physical graviton two-point functions in de Sitter spacetime

Abstract

It is known that the covariant graviton two-point function in de Sitter spacetime is infrared-divergent for some choices of gauge parameters. On the other hand, it is also known that there are no infrared divergences requiring an infrared cutoff for the physical graviton two-point function for this spacetime in the transverse-traceless-synchronous gauge in the global coordinate system. We show in this paper that the covariant graviton Wightman two-point function with two gauge parameters is equivalent to the physical one in the global coordinate system in the sense that they produce the same two-point function of any local gauge-invariant tensor linear in the graviton field such as the linearized Weyl tensor. This confirms the fact, pointed out decades ago, that the infrared divergences of the graviton two-point function in the covariant gauge for some choices of gauge parameters are a gauge artifact in the sense that they do not contribute to the Wightman two-point function of any local gauge-invariant tensor field in linearized theory.