QUANTUM-FIELD THEORY IN THE DE SITTER UNIVERSE

We present a study of quantum scalar fields on de Sitter (dS) space-ti me based on analyticity in the complexified Riemannian manifold; a new expansion of the linear fields in terms of coordinate independent dS plane waves and an explicit form of the propagators at real or imagina ry times are given. Our approach controls the thermal properties and t he zero-curvature limit of the fields; it provides a general setting f or interacting fields, in which some steps are taken: a Kallen-Lehmann type formula for complete propagators and a treatment of a class of s elf-energy diagrams and their resummation.