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We discuss the quantization of linearized gravity in the background de Sitterspacetime using a gauge-invariant formalism to write the perturbedgravitational field in the static patch. This field is quantized after fixingthe gauge completely. The response rate of this field to monochromaticmultipole sources is then computed in the thermal equilibrium state with thewell known Gibbons-Hawking temperature. We compare this response rate with theone obtained in the Bunch-Davies-like vacuum state defined in the Poincar\'epatch. These response rates are found to be the same as expected. Thisagreement serves as a verification of the infrared finite graviton two-pointfunction in the static patch of de Sitter spacetime found previously.

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