LINEARIZED GRAVITY IN DESITTER 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 a 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 in this paper is a preliminary for the study of quantum linearization instabilities, which will be reported elsewhere.