Quantum field theory in the de sitter universe

We present a study of quantum scalar fields on de Sitter (dS) space-time 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 imaginary times are given. Our approach controls the thermal properties and the zero-curvature limit of the fields; it provides a general setting for interacting fields, in which some steps are taken: a K\"allen-Lehmann type formula for complete propagators and a treatment of a class of self-energy diagrams and their resummation.