Speaker
Description
In the stochastic $\delta N$ formalism, the statistics of the primordial density perturbations can be mapped onto the first-passage distribution of the underlying stochastic process. In this talk, I will present a general framework to evaluate the rare-event tail of this distribution, based on a saddle-point approximation of the associated path integral.
I will show that, at leading order, this description is equivalent to a more fundamental formulation in terms of the Schwinger-Keldysh path integral, in which integrating out short-wavelength modes yields an influence functional encoding the noise statistics of Starobinsky's stochastic approach. I will also show how this methodology can be exploited for importance sampling, providing an efficient numerical handle on rare events.
Finally, I will present gradient corrections to the instanton equations, both in analytically tractable models and in more realistic potentials, and discuss their implications for primordial black hole production.