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The talk is intended as a pedagogical introduction to some current topics in quantum field theory in cosmological backgrounds.
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 methods.