Aurora Ireland (Stanford) - A Tail of Two Modes: PBH Formation Beyond the Stochastic Approximation

Aurora Ireland
Please note this event occurred in the past.
September 19, 2025 2:30 pm - 4:00 pm ET
ACFI Seminar
LGRT 1033

A Tail of Two Modes: PBH Formation Beyond the Stochastic Approximation

Aurora Ireland (Stanford) 
 
In standard calculations of primordial black hole (PBH) formation, the curvature perturbation is treated as a stochastic random variable. This is a valid approximation when the growing mode dominates, as is the case on superhorizon scales during slow-roll inflation. However, PBH formation typically involves a revival of the decaying mode, and near the transition where the two solutions exchange dominance, interference effects can become important, potentially invalidating the stochastic approach. Since PBH production is sensitive to the tail of the probability distribution, even small departures from Gaussianity can dramatically alter predictions. 

 
Employing the EFT of inflation and working to all orders in perturbation theory, we analyze the dynamics of quantum fluctuations in an inflationary background which deviates transiently from slow roll. In the far superhorizon limit, we construct the Wigner function W, whose positivity can be used as a diagnostic of the validity of the stochastic approach. We find that W becomes highly oscillatory and negative in certain regions of phase space --- a hallmark of quantum interference and non-classicality. We characterize how the Wigner negativity correlates with various model parameters as well as with the size of the linear theory growing and decaying modes, identifying regions in parameter space where the stochastic approach breaks down. Remarkably, we find that these non-perturbative quantum effects persist even upon the return to slow-roll evolution, signaling a kind of "classical-to-quantum transition" for the affected modes. Among our other results, we conclude that the squeezing picture --- or equivalently, the size of linear theory growing and decaying modes --- is insufficient to diagnose classicality.