Abstract
It is known that all the physical states in linearized gravity are required to be invariant under the continuous isometries of the background spacetime if it is spatially compact. For example, all the physical states in linearized gravity in de Sitter spacetime are required to be SO(4, 1) invariant. A detailed derivation of SO(4, 1) invariance of the physical state is presented. Also, it is found that normal ordering of operators is unnecessary in the constraints which demand SO(4, 1) invariance. Then it is proved that there are no normalizable SO(4, 1)-invariant states other than the vacuum state in the Fock space. This appears to suggest that there would be no dynamics in de Sitter spacetime. A step towards a possible resolution of this paradox will be presented in the sequel to this article.
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