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

Abstract

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

6 pages, revised and extended version of a talk; minor errors corrected; proof for de Sitter space improved

References in corpus (2)

• Fluctuating geometries, q-observables, and infrared growth in inflationary spacetimes
• On cosmic hair and "de Sitter breaking" in linearized quantum gravity

Cited by in corpus (4)

• Mode-sum construction of the covariant graviton two-point function in the Poincaré patch of de Sitter space
• The Weyl tensor correlator in cosmological spacetimes
• On cosmic hair and "de Sitter breaking" in linearized quantum gravity
• Gauge invariants of linearized gravity with a general background metric