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Register a new userDissecting the growth of the power spectrum for primordial black holes
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We consider the steepest rate at which the power spectrum from single field inflation can grow, with the aim of providing a simple explanation for the $k^4$ growth found recently. With this explanation in hand we show that a slightly steeper $k^5 (log k )^2$ growth is in fact possible. Moreover, we argue that the power spectrum after a steep growth cannot immediately decay, but must remain large for the $k$ modes which exit during a $sim2$ e-fold period. We also briefly consider how a strong growth can affect the spectral index of longer wavelengths preceding the growth, and show that even the conversion of isocurvature modes likely cannot lead to a stronger growth. These results have implications for the formation of primordial black holes, and other phenomena which require a large amplitude of power spectrum at short scales.
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We study the effect of dark matter (DM) being encapsulated in primordial black holes (PBHs) on the power spectrum of density fluctuations $P(k)$; we also look at its effect on the abundance of haloes and their clustering. We allow the growth of Poisson fluctuations since matter and radiation equality and study both monochromatic and extended PBH mass distributions. We present updated monochromatic black hole mass constraints by demanding $<10%$ deviations from the $Lambda$ cold dark matter power spectrum at a scale of $k=1$hMpc$^{-1}$. Our results show that PBHs with masses $>10^4$h$^{-1}M_odot$ are excluded from conforming all of the DM in the Universe. We also apply this condition to our extended Press-Schechter (PS) mass functions, and find that the Poisson power is scale dependent even before applying evolution. We find that characteristic masses $M^*leq10^2 $h$^{-1}M_odot$ are allowed, {leaving only two characteristic PBH mass windows of PS mass functions when combining with previous constraints, at $M^*sim10^2$h$^{-1}M_odot$ and $sim10^{-8}$h$^{-1}M_odot$ where all of the DM can be in PBHs. The resulting DM halo mass functions within these windows are similar} to those resulting from cold dark matter made of fundamental particles. However, as soon as the parameters produce unrealistic $P(k)$, the resulting halo mass functions and their bias as a function of halo mass deviate strongly from the behaviour measured in the real Universe.
We modify the procedure to estimate PBH abundance proposed in arXiv:1805.03946 so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure, we focus on peaks of the Laplacian of the curvature perturbation $triangle zeta$ and use the values of $triangle zeta$ and $triangle triangle zeta $ at each peak to specify the profile of $zeta$ as a function of the radial coordinate while the values of $zeta$ and $triangle zeta$ are used in arXiv:1805.03946. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure in arXiv:1805.03946. Furthermore, the new procedure allows us to estimate PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the $k$-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the $k$-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.
We calculate the exact formation probability of primordial black holes generated during the collapse at horizon re-entry of large fluctuations produced during inflation, such as those ascribed to a period of ultra-slow-roll. We show that it interpolates between a Gaussian at small values of the average density contrast and a Cauchy probability distribution at large values. The corresponding abundance of primordial black holes may be larger than the Gaussian one by several orders of magnitude. The mass function is also shifted towards larger masses.
Primordial black holes might comprise a significant fraction of the dark matter in the Universe and be responsible for the gravitational wave signals from black hole mergers observed by the LIGO/Virgo collaboration. The spatial clustering of primordial black holes might affect their merger rates and have a significant impact on the constraints on their masses and abundances. We provide some analytical treatment of the primordial black hole spatial clustering evolution, compare our results with some of the existing N-body numerical simulations and discuss the implications for the black hole merger rates. If primordial black holes contribute to a small fraction of the dark matter, primordial black hole clustering is not relevant. On the other hand, for a large contribution to the dark matter, we argue that the clustering may increase the late time Universe merger rate to a level compatible with the LIGO/Virgo detection rate. As for the early Universe merger rate of black hole binaries formed at primordial epochs, clustering alleviates the LIGO/Virgo constraints, but does not evade them.
The properties of primordial curvature perturbations on small scales are still unknown while those on large scales have been well probed by the observations of the cosmic microwave background anisotropies and the large scale structure. In this paper, we propose the reconstruction method of primordial curvature perturbations on small scales through the merger rate of binary primordial black holes, which could form from large primordial curvature perturbation on small scales.
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