Primordial black holes from metric preheating: mass fraction in the excursion-set approach

After inflation, the oscillations of the inflaton at the bottom of its potential source a parametric instability in the equation of motion of scalar perturbations. In a recent paper by Martin et al. 2020, it was shown that the production of ultra-light PBHs from this instability is so efficient that they can quickly come to dominate the universe content. However their abundance is usually computed by assuming that they are rare objects that are formed at around a single scale, and the probability that a given region of the universe ends up in a black hole can be inferred from the knowledge of the primordial curvature power spectrum at that scale. Such an approach may however fail in cases where PBHs are abundantly produced, and/or if they arise over a wide range of masses.

In the present seminar, I will first briefly describe the mechanism of metric preheating and the production of PBHs that is associated to it. Then I will give a short introduction on the calculation of the mass fraction and more particularly the excursion set formalism. This framework translates the estimation of a mass fraction to the study of a Langevin equation; more particularly to the first crossing distribution of a Langevin trajectory with a moving barrier. Finally, I will present the result of applying this formalism to the calculation of the mass fraction of PBHs arising from metric preheating.