arXiv : From Primordial Black Holes Abundance to Primordial Curvature Power Spectrum (and back)

Kalaja, Alba; Bartolo, Nicola; Matarrese, Sabino; Bellomo, Nicola; Bertacca, Daniele; Verde, Licia; Musco, Ilia; Raccanelli, Alvise

doi:10.1088/1475-7516/2019/10/031

Article
Report number	arXiv:1908.03596
Title	From Primordial Black Holes Abundance to Primordial Curvature Power Spectrum (and back)
Author(s)	Kalaja, Alba (Padua U., Astron. Dept. ; ICC, Barcelona U. ; U. Groningen, VSI) ; Bellomo, Nicola (ICC, Barcelona U. ; U. Barcelona (main)) ; Bartolo, Nicola (Padua U., Astron. Dept. ; INFN, Padua ; Padua Observ.) ; Bertacca, Daniele (Padua U., Astron. Dept. ; INFN, Padua) ; Matarrese, Sabino (Padua U., Astron. Dept. ; INFN, Padua ; Padua Observ. ; GSSI, Aquila) ; Musco, Ilia (ICC, Barcelona U.) ; Raccanelli, Alvise (ICC, Barcelona U. ; CERN) ; Verde, Licia (ICC, Barcelona U. ; ICREA, Barcelona)
Publication	2019-10-11
Imprint	2019-08-09
Number of pages	52
Note	52 pages, 9 figures. Matches the published version
In:	JCAP 1910 (2019) 031
DOI	10.1088/1475-7516/2019/10/031 (publication)
Subject category	astro-ph.CO ; Astrophysics and Astronomy
Abstract	In the model where Primordial Black Holes (PBHs) form from large primordial curvature (C) perturbations, i.e., CPBHs, 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.
Copyright/License	Preprint: (License: arXiv nonexclusive-distrib 1.0) Publication: 2019 IOP Publishing Ltd and Sissa Medialab

$Maximum allowed amplitude of the primordial curvature power spectrum. Current (solid lines) and forecasted (dashed lines) constraints from the cosmic microwave background (CMB, $1\sigma\ \mathrm{CL}$)~\cite{akrami:planckng2018}, spectral distortions (FIRAS and PIXIE)~\cite{chluba:powerspectrumconstraints}, gravitational waves (PTA, SKA and LISA)~\cite{byrnes:steepestgrowth}, Silk damping (SD)~\cite{jeong:powerspectrumconstraints}, quasar light curves (QSO)~\cite{karami:powerspectrumconstraints} and PBHs (the thin and thick orange lines correspond to Ref.~\cite{josan:powerspectrumconstraints} and \cite{satopolito:powerspectrumconstraints}, respectively). The red shaded region is the result of this work. It shows upper limits from PBH abundance for the range of profiles with shape parameter~$\alpha\in \left[0.15,30.0\right]$, considering the most recent constraints on the maximum allowed fraction of PBHs. We report our constraint for PBHs masses ranging from~$M_\mathrm{PBH}=10^{-17}\ M_\odot$ ($k_t\simeq 10^{15}\ \mathrm{Mpc}^{-1}$) to~$M_\mathrm{PBH}=10^{3}\ M_\odot$ ($k_t\simeq 10^{5}\ \mathrm{Mpc}^{-1}$).$ $Shape of the reconstructed primordial curvature power spectra for steep (\textit{left panel}) and flat profiles (\textit{right panel}). In both cases we report the profile for~$M_\mathrm{PBH}=10^{-15}\ M_\odot$ (light blue line) and~$M_\mathrm{PBH}=10\ M_\odot$ (red line). To the right of the peak, the profile is reconstructed using equation~\eqref{eq:reconstruction_curvature_powerspectrum}, and to the left is computed assuming different model for the growth of the power spectrum (see text for details).$ $Linear and non-linear overdensity profile of equation~\eqref{eq:overdensity_cosmo_metric} on super-horizon scales, for a steep profiles with $\alpha=0.5$ (\textit{left panel}) and a flat profile $\alpha=30$ (\textit{right panel}). Solid lines indicate overdensity $(\delta_\mathrm{peak}>0)$ while dashed lines indicate underdensities $(\delta_\mathrm{peak}<0)$. The profile is showed in units of the typical scale of the perturbation $r_t=\hat{r}_m$ in the linear approximation or $r_t=\hat{r}_m e^{-\zeta_\mathrm{peak}(\hat{r}_m)}$ in the non-linear case. In both cases the non-linear corrections damps and shrink the overdensity profile significantly with respect to the linear case. We use $\mathcal{A}_\mathrm{peak} r^2_t = 5.18,\ 0.99$ for $\alpha=0.5,\ 30$, respectively.$ Show more plots

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