Linearized gravity in de Sitter spacetime as a representation of SO(4, 1)

The solutions to the linearized Einstein equation in de Sitter spacetime are explicitly written down. Their group-theoretical properties are examined with an emphasis on the way these solutions form a unitary representation of the de Sitter group, SO(4, 1). For this purpose of duality operator acting on them is defined. This operator is analogous to the helicity operator on gravitons in Minkowski spacetime. It is found that the self-dual solutions and the anti-self-dual solutions separately form unitary irreducible representations. The work presented is a preliminary for the study of quantum linearization instabilities, which will be reported elsewhere.