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

摘要

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