Langevin equation, Markovian process, multiplicative noise, Fokker-Planck equation, Schwinger-Keldysh formalism and much more... During this seminar, almost organised as a lecture, you will embark on a journey into the world of stochastic processes, with focus on their applications in the early Universe in the context of so-called stochastic inflation. We will begin by discussing how stochasticity emerges from the coarse-graining procedure, necessary to describe the effective dynamics of the largest cosmological scales that are affected by the quantum nature of the small-scale fluctuations.

Upcoming Large-Scale Structure surveys will likely become the next leading sources of cosmological information, making it crucial to have a precise understanding of the influence of baryons on cosmological observables. The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a consistent way to predict the clustering of dark matter and baryons on large scales, where their leading corrections in perturbation theory are given by a simple and calculable functional form even after the onset of baryonic processes.

Departures of inflation from the single-field slow-roll paradigm, also known as “features”, are common in ultraviolet completions of inflation. These departures can be significant at small scales where Cosmic Microwave Background data is not constraining. I will explain how such features during inflation can be tested through their gravitational wave signal. In particular, I will show that features lead to a characteristic oscillation in the stochastic gravitational wave background.