Primordial black holes and stochastic inflation beyond slow roll: I -- noise matrix elements

Understand

Primordial Black Holes (PBHs) may form in the early Universe, from the gravitational collapse of large density perturbations, generated by large quantum fluctuations during inflation.

• Since PBHs form from rare over-densities, their abundance is sensitive to the tail of the primordial probability distribution function (PDF) of the perturbations.
• It is therefore important to calculate the full PDF of the perturbations, which can be done non-perturbatively using the 'stochastic inflation' framework.
• In single field inflation models generating large enough perturbations to produce an interesting abundance of PBHs requires violation of slow roll.