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

TL;DR

This paper demonstrates that the infrared divergences in the covariant graviton two-point function in de Sitter spacetime are gauge artifacts, showing their equivalence to the physical two-point function for gauge-invariant tensors.

Contribution

It proves the gauge equivalence of covariant and physical graviton two-point functions in de Sitter spacetime, clarifying the nature of infrared divergences.

Findings

Covariant and physical two-point functions produce identical results for gauge-invariant tensors.

Infrared divergences in covariant graviton two-point functions are gauge artifacts.

The equivalence holds in the global coordinate system for the transverse-traceless-synchronous gauge.

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 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.