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The two-point Wightman function of the free photon field defined in agauge-invariant manner is known to be equivalent to the field-strengthtwo-point function in any spacetime that is topologically trivial. We show thatthe gauge-invariant graviton two-point function defined in a similar manner isequivalent to the Weyl-tensor two-point function in Minkowski space and in thePoincare patch of de Sitter space. This implies that in the Poincare patch ofde Sitter space the gauge-invariant graviton two-point function decays like(distance)^(-4) as a function of coordinate distance for spacelike separation.

Equivalence between the Weyl-tensor and gauge-invariant graviton two-point functions in Minkowski and de Sitter spaces