The next cosmology seminar takes place on Friday 13th of March, room E349 at 2:00pm. We will have the pleasure to listen to Pierre Auclair from the Institut d’Astrophysique de Paris (IAP, France).
At 2:00pm, room E349, Pierre Auclair will be talking about
Excursion-set for Primordial Black Holes: white noise and moving barrier
I will introduce pedagogically the Excursion-Set formalism, a framework in which the mass distribution of primordial black holes (PBHs) is derived from the first-passage time of a random walk describing the density contrast as the coarse-graining scale varies. In particular, I will address in detail two recent criticisms/remarks that have been raised about this approach. First, it was argued that the random walks are subject to colored (i.e. correlated over time) noise, making the first-passage-time problem cumbersome. We show that this arises from an incorrect separation of drift and noise when sampling on the Hubble-crossing surface: if Fourier modes are uncorrelated, the noise is strictly white. Moreover, sampling along the Hubble-crossing surface precludes using the density dispersion as a time variable, explaining the reported pathologies. Sampling instead on a synchronous surface removes both issues. This requires solving a first-passage-time problem with a moving barrier, for which we provide an efficient numerical framework. Second, it was suggested that cloud-in-cloud (i.e. that large black holes may engulf smaller ones) is irrelevant for PBHs and that the excursion set is therefore not needed. While valid for widely separated scales, this statement fails for broad power spectra with enhanced continua of modes. We further show that Press-Schechter estimates neglecting boundary evolution can break down even without cloud-in-cloud effects [1].