Interacting scalar fields in de Sitter space

Abstract

We investigate the massless $\lambda \phi^4$ theory in de~Sitter space. It is unnatural to assume a minimally coupled interacting scalar field, since $\xi=0$ is not a fixed point of the renormalization group once interactions are included. In fact, the only case where perturbation theory can be trusted is when the field is non-minimally coupled at the minimum of the effective potential. Thus, in perturbation theory, there is no infrared divergence associated with this scalar field.