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Quantum field theory in expanding universes allows us to
describe correlations at the end of inflation/beginning of the hot Big
Bang, which sets the seeds for the subsequent evolution of the
universe. However, such correlations turn out to suffer from infra-red
divergencies whenever sufficiently light states are involved. Despite
recent works point toward a resolution of this issue for the
leading divergencies in de Sitter space-time via resummation, with the
resummed probability distribution being compatible with the stochastic
inflation proposal, a fundamental undestanding is still missing. In
this talk I will describe a novel approach to this issue discussing the
possibility of defining infrared safe observables.