Fluctuation and dissipation dynamics in the early universe
The aim of this thesis is to study the effects of fluctuation and dissipation dynamics in Early Universe cosmology. The formal description of the Early Universe relies on cosmological fields that, in general, are not completely isolated from and, therefore, interact with their environment. These interactions might lead to two non-negligible effects. Fluctuations, acting as stochastic forces, tend to perturb the motion of the field. In addition, some fraction of the energy is transferred from the field to other degrees of freedom, corresponding to dissipation. We are interested in three situations where fluctuation and dissipation dynamics plays a significant role for cosmology. After a brief review of the prevailing model of cosmology, the Standard Big Bang Model, we study the formation of embedded defects. This particular realization of topological defects is not stable by construction. While considering one of the simplest examples, the pion string, we show that the interactions with a thermal and dense medium might, in some circumstances, provide a stabilization mechanism. We then turn our interest to the warm realization of inflation. Ideas borrowed from the renormalization group are applied to warm inflation in order to define universality classes among the different models of inflation. Beyond the identification of universality, this approach is well-suited for an analytical treatment of warm inflation and helps in the characterization of the possible smooth transition to the radiation-dominated regime. Finally, we extend the Kramers problem to quantum field theory. In the presence of fluctuation and dissipation dynamics, there is a non-vanishing probability for a field initially located at a minimum of its potential to escape from the well. We define and derive the escape rate for a scalar field, due to thermal fluctuations, and discuss the applications for cosmology.