From Primordial Black Holes Abundance to Primordial Curvature Power Spectrum (and back). (arXiv:1908.03596v1 [astro-ph.CO])

From Primordial Black Holes Abundance to Primordial Curvature Power Spectrum (and back). (arXiv:1908.03596v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Kalaja_A/0/1/0/all/0/1">Alba Kalaja</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Bellomo_N/0/1/0/all/0/1">Nicola Bellomo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Bartolo_N/0/1/0/all/0/1">Nicola Bartolo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Bertacca_D/0/1/0/all/0/1">Daniele Bertacca</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Matarrese_S/0/1/0/all/0/1">Sabino Matarrese</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Musco_I/0/1/0/all/0/1">Ilia Musco</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Raccanelli_A/0/1/0/all/0/1">Alvise Raccanelli</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Verde_L/0/1/0/all/0/1">Licia Verde</a>

In the model where Primordial Black Holes (PBHs) form from large primordial
perturbations, constraints on PBH abundance provide in principle constraints on
the primordial curvature power spectrum. This connection however depends
necessarily on the details of PBH formation mechanism. In this paper we
provide, for the first time, constraints on the primordial curvature power
spectrum from the latest limits on PBH abundance, taking into account all the
steps from gravitational collapse in real space to PBH formation. In
particular, we use results from numerical relativity simulations and peak
theory to study the conditions for PBH formation for a range of perturbation
shapes, including non-linearities, perturbation profile and a careful treatment
of smoothing and filtering scales. We then obtain updated PBH formation
conditions and translate that into primordial spectrum constraints for a wide
range of shapes and abundances. These updated constraints cover a range of
scales not probed by other cosmological observables. Our results show that the
correct and accurate modelling of non-linearities, filtering and typical
perturbation profile, is crucial for deriving meaningful cosmological
implications.

In the model where Primordial Black Holes (PBHs) form from large primordial
perturbations, constraints on PBH abundance provide in principle constraints on
the primordial curvature power spectrum. This connection however depends
necessarily on the details of PBH formation mechanism. In this paper we
provide, for the first time, constraints on the primordial curvature power
spectrum from the latest limits on PBH abundance, taking into account all the
steps from gravitational collapse in real space to PBH formation. In
particular, we use results from numerical relativity simulations and peak
theory to study the conditions for PBH formation for a range of perturbation
shapes, including non-linearities, perturbation profile and a careful treatment
of smoothing and filtering scales. We then obtain updated PBH formation
conditions and translate that into primordial spectrum constraints for a wide
range of shapes and abundances. These updated constraints cover a range of
scales not probed by other cosmological observables. Our results show that the
correct and accurate modelling of non-linearities, filtering and typical
perturbation profile, is crucial for deriving meaningful cosmological
implications.

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