We study the linearized gravity theory in the Newman-Unti gauge in the near horizon region of the de Sitter spacetime. The linearized Einstein equation involves the cosmological constant. The near horizon symmetry consists of near horizon supertranslation and near horizon superrotation. We compute the near horizon supertranslation charge and find the proper near horizon fall-off conditions which uncover a soft graviton theorem from the Ward identity of the near horizon supertranslation.
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Mao et al. (2024) studied this question.
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