Primordial black holes from stochastic tunnelling

If the inflaton gets trapped in a local minimum of its potential shortly before end inflation, it escapes by building up quantum fluctuations process known as stochastic tunnelling. In this work we study cosmological produced such scenario, and how likely they are to form Primordial Black Holes (PBHs). This is done using stochastic-$\delta N$ formalism, which allows us reconstruct highly non-Gaussian tails distribution function number $e$-folds spent false-vacuum state. We explore two different toy models, both analytically numerically, order identify properties do or not depend on details profile. find that when barrier small enough compared width, $\Delta V/V < \Delta\phi^2/M_{\text{Pl}}^2$, can be approximated being flat between extrema, so results previously obtained "flat well'' apply. Otherwise, V/M_{\text{Pl}}^4$, PBH abundance depends exponentially height barrier, > V/M_{\text{Pl}}^4$ super-exponentially ( i.e. exponential an exponential) height. later case PBHs massively produced. quantify much inflection points need fine-tuned. deep false vacuum, also slow-roll violations typically encountered unless close linear. motivates further investigations generalise our approach non-slow-roll setups.