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Abstract |
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. Special features of stochastic calculus
and stochastic differential equations will be highlighted and applications to both
situations of cosmological interest as well as to formal QFT results in curved
spacetimes will be explained. After this very long introduction, I will summarise
the three years of work that it took us to consistently extend the stochastic
formalism to multifield models of inflation and solve the so-called inflationary
stochastic anomalies, intrinsically related to the discretisation ambiguity of
stochastic differential equations and the quantum nature of cosmological
perturbations. |
