  We show that dissipative effects have a significant impact on the evolution
of cosmological scalar fields, leading to friction, entropy production and
field fluctuations. We explicitly compute the dissipation coefficient for
different scalar fields within the Standard Model and some of its most widely
considered extensions, in different parametric regimes. We describe the generic
consequences of fluctuation-dissipation dynamics in the post-inflationary
universe, focusing in particular on friction and particle production, and
analyze in detail two important effects. Firstly, we show that dissipative
friction delays the process of spontaneous symmetry breaking and may even damp
the the motion of a Higgs field sufficiently to induce a late period of warm
inflation. Along with dissipative entropy production, this may parametrically
dilute the abundance of dangerous thermal relics. Secondly, we show that
dissipation can generate the observed baryon asymmetry without symmetry
restoration, and we develop in detail a model of dissipative leptogenesis. We
further show that this generically leads to characteristic baryon isocurvature
perturbations that can be tested with CMB observations. This work provides a
fundamental framework to go beyond the leading thermal equilibrium
semi-classical approximation in addressing fundamental problems in modern
cosmology.
