[Paper Review] Simulation of Primordial Black Holes with large negative non-Gaussianity

Albert Escrivà, Yuichiro Tada+2 more|arXiv (Cornell University)|Feb 2, 2022

Cosmology and Gravitation TheoriesPhysics and Astronomy90 references73 citations

TL;DR

This paper performs high-precision numerical simulations of primordial black hole (PBH) formation in a radiation-dominated universe with local-type non-Gaussianity, parameterized by negative fNL. Contrary to previous analytical estimates using the universal averaged critical compaction function (¯Cc = 2/5), the simulations confirm type I PBH formation even for fNL ≲ −0.336, demonstrating that this universal threshold fails for certain non-Gaussian profiles. Instead, the q-parameter fitting formula provides a more robust analytical estimate with sub-2% error for fNL ≳ −1.

ABSTRACT

In this work, we have performed numerical simulations of primordial black hole (PBH) formation in the Friedman-Lema\^itre-Robertson-Walker universe filled by radiation fluid, introducing the local-type non-Gaussianity to the primordial curvature fluctuation. We have compared the numerical results from simulations with previous analytical estimations on the threshold value for PBH formation done in the previous paper arXiv:2109.00791, particularly for negative values of the non-linearity parameter $f_{ m NL}$. Our numerical results show the existence of PBH formation of (the so-called) type I also in the case $f_{ m NL} \lesssim -0.336$, which was not found in the previous analytical expectations using the critical averaged compaction function. In particular, although the universal value for the averaged critical compaction function $\bar{\mathcal{C}}_{c}=2/5$ found previously in the literature is not satisfied for all the profiles considered in this work, an alternative direct analytical estimate has been found to be roughly accurate to estimate the thresholds, which gives the value of the critical averaged density with a few $\%$ deviation from the numerical one for $f_{ m NL}\gtrsim -1$.

Motivation & Objective

• To test the validity of the universal averaged critical compaction function (¯Cc = 2/5) for PBH formation in the presence of large negative local-type non-Gaussianity (fNL).
• To investigate whether type I PBHs can form when analytical estimates based on ¯Cc = 2/5 predict no formation (for fNL ≲ −0.336).
• To assess the robustness of the q-parameter fitting formula as an alternative analytical threshold estimator under strong non-Gaussianity.
• To update the PBH mass function and abundance predictions using the newly identified parameter space for PBH formation with negative fNL.

Proposed method

• Numerical simulations of PBH formation in a Friedmann–Lemaître–Robertson–Walker (FLRW) universe filled with radiation, using a substantially improved code compared to prior works.
• Implementation of a monochromatic power spectrum with a single wavenumber k* to model localized curvature perturbations.
• Incorporation of local-type non-Gaussianity via the fNL parameter, modifying the primordial curvature perturbation as ζ(r) = µ sinc(k*r) + (3/5)fNL µ² sinc²(k*r).
• Use of the q-parameter fitting formula (Eq. 3.8) to analytically estimate the critical threshold for PBH formation, independent of the universal ¯Cc = 2/5 assumption.
• Comparison of numerical PBH formation thresholds with both the averaged compaction function approach and the q-parameter fit across a range of fNL values.
• Statistical derivation of the PBH mass function using peak theory, with the critical behavior M ∝ (µ − µc)^γ and γ ≈ 0.36, and normalization to the current dark matter density.

Experimental results

Research questions

• RQ1 Does PBH formation (specifically type I) occur for fNL ≲ −0.336, as predicted by the universal averaged critical compaction function ¯Cc = 2/5?
• RQ2 How accurate is the q-parameter fitting formula (δc(q)) in estimating the PBH formation threshold for large negative fNL values?
• RQ3 What is the impact of non-Gaussianity on the PBH mass function and total abundance, particularly in the newly accessible region fNL ≲ −0.336?
• RQ4 Can the failure of the universal ¯Cc = 2/5 assumption be attributed to specific profile-dependent behaviors in non-Gaussian curvature fluctuations?

Key findings

• Numerical simulations confirm the formation of type I PBHs for fNL ≲ −0.336, contradicting the analytical prediction based on the universal ¯Cc = 2/5 threshold.
• The averaged critical compaction function ¯Cc is not universally 2/5 for all non-Gaussian profiles; for fNL ≲ −0.336, it deviates significantly, indicating a breakdown of the universal assumption.
• The q-parameter fitting formula (Eq. 3.8) provides a robust analytical estimate of the threshold, with less than 2% deviation from numerical results for fNL ≳ −1.
• For fNL ≲ −1, the fNL expansion becomes questionable, and the q-parameter fit begins to lose accuracy, suggesting a limit to its applicability.
• The PBH mass function is updated to include the region fNL ≲ −0.336, with the total PBH abundance ftot_PBH reaching unity when σ²₀ is tuned accordingly for fNL = −1.
• The critical point where the threshold µc intersects the boundary (3/5)µfNL = −1/2 occurs at fNL ≈ −1.01, marking a transition in the formation regime.