Primordial black holes (PBHs) are a major candidate for dark matter, expected to form from the collapse of large density fluctuations generated during inflation. Their abundance is highly sensitive to non-linear effects, some of which can be described through the δN formalism. This approach models the universe as a set of locally homogeneous patches evolving independently throughout inflation. However, accounting for the spatial correlations between these patches is crucial to predicting the spatial contribution of PBHs and the formation of clusters. In this talk, after reviewing the δN formalism, I will show how to include spatial correlations within this framework. As an illustration, I will discuss the ultra-slow-roll model and compute the curvature perturbation ζ -necessary to determine PBH formation- and its spatial correlations at the end of inflation. In the future, this could enable the prediction of PBH binaries and clusters, which may leave observable imprints such as gravitational waves. 

Biography

Danilo did a joint PhD between Universtity Paris-Saclay in France and Jagiellonian University in Poland where he studied aspects of quantum gravity and non-linear effects in cosmology, in particular during inflation, from 2019 to 2023. After that, he joined the Department of Physics of Kyoto University as a JSPS fellow. His main research interest center on cosmological inflation, particularly in the non-linear regime of cosmological perturbations and its relation with Primordial Black Holes and Gravitational Waves.

Inviter: Shi Pi