The Gibbons-Hawking radiation of gravitons in the Poincar\'e and static patches of de Sitter spacetime

TL;DR

This paper quantizes linearized gravity in de Sitter spacetime, computes the response rate of gravitons to sources in different patches, and verifies the consistency of the graviton two-point function across these regions.

Contribution

It introduces a gauge-invariant formalism for quantizing gravitons in de Sitter space and confirms the infrared finiteness of the graviton two-point function in the static patch.

Findings

Response rates in static and Poincaré patches agree as expected.

Verification of the infrared finiteness of the graviton two-point function.

Consistency of graviton response across different de Sitter patches.

Abstract

We discuss the quantization of linearized gravity in the background de Sitter spacetime using a gauge-invariant formalism to write the perturbed gravitational field in the static patch. This field is quantized after fixing the gauge completely. The response rate of this field to monochromatic multipole sources is then computed in the thermal equilibrium state with the well known Gibbons-Hawking temperature. We compare this response rate with the one obtained in the Bunch-Davies-like vacuum state defined in the Poincar\'e patch. These response rates are found to be the same as expected. This agreement serves as a verification of the infrared finite graviton two-point function in the static patch of de Sitter spacetime found previously.