Massless minimally coupled scalar field in de Sitter space

Abstract

We quantize the massless minimally coupled scalar field in de Sitter space, and find a one-complex-parameter family of O(4)-invariant Hadamard Fock vacua which break de Sitter invariance. The different Fock spaces corresponding to the different choices of vacuum are subspaces of a single space of states. We make some remarks about the existence of E(3)- and O(1,3)-invariant Fock vacuum states.