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In the first part, I will discuss the thermal and dissipative properties of quantum fields in de Sitter space, focusing on the KMS condition and the fluctuation–dissipation theorem, with an outlook toward generalizations to an inflationary context.
In the second part, I will present a systematic framework for computing loop corrections — including finite parts — to cosmological correlators. Particular emphasis will be placed on the renormalization procedure and on the comparison between different regularization schemes. The talk will conclude with a brief discussion of current applications.