Clustering of primordial black holes from quantum diffusion during inflation
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During the inflationary phase, quantum vacuum fluctuations are amplified on astrophysical scales, leaving imprints in the anisotropies of the cosmic microwave background and seeding the formation of large-scale structures. If these perturbations are sufficiently large, they can also collapse to form primordial black holes (PBHs).
A crucial property of PBHs is their spatial distribution, therefore a central point is to characterise their initial clustering, which influences their clustering evolution throughout cosmic history. If PBHs are created from the collapse of large Gaussian fluctuations, they are initially unclustered. However, the presence of non-Gaussianities is expected to change this scenario.
In this seminar, I will show how to derive the clustering of PBHs in the presence of non-perturbative non-Gaussianities using the stochastic-delta N formalism. I will explain how to reconstruct the two-point statistics of the curvature perturbation in stochastic inflation, consistently including volume-weighting effects, to obtain the reduced correlation of PBHs. The outcome of this approach shows that, in the exponential tail, the reduced correlation is independent of the formation threshold value, which contrasts with Gaussian statistics. This result reveals a universal clustering profile for all structures forming in the exponential tails.