Primordial Black Holes from Primordial Voids

TL;DR

This work proposes primordial voids as a novel channel for primordial black hole formation from negative curvature perturbations. It uses full numerical relativity within the BSSN framework to track PV rebounces after Hubble re-entry and identify critical thresholds and mass scaling across equations of state $p=\omega\rho_{ m fl}$. The key results show PVs can collapse to PBHs above a negative-amplitude threshold $\mu_c^{(-)}$, with mass following a critical scaling $M_{ m PBH}/M_\times = K|\mu-\mu_c|^{\gamma}$ and a universal exponent $\gamma\simeq 0.36$ for $\omega\simeq 1/3$, while thresholds and dynamics depend on geometry (type I/II) and core curvature. The findings imply PVs could alter PBH abundances and leave distinct cosmological signatures, motivating further study of PV shapes, non-Gaussianities, and scalar-field epochs.

Abstract

Primordial black holes (PBHs) are a compelling dark matter candidate and a unique probe of small-scale cosmological fluctuations. Their formation is usually attributed to large positive curvature perturbations, which collapse upon Hubble re-entry during radiation domination. In this work we investigate instead the role of negative curvature perturbations, corresponding to the growth of primordial void (PV) like regions. Using numerical relativity simulations, we show that sufficiently deep PV can undergo a nonlinear rebounce at the center, generating an effective overdensity that eventually collapses into a PBH. We determine the critical threshold for this process for a variety of equations of state, and demonstrate that the resulting black holes obey a scaling relation analogous to the standard overdensity case. These results establish primordial voids as a novel channel for PBH formation and highlight their potential impact on PBH abundances and cosmological signatures.

Figures (5)

• Figure 1: Amplitude thresholds for type-A PBH formation across different equations of state $\omega$. Black dots denote results from numerical relativity simulations, connected by a solid black line (quadratic interpolation) representing the separatrix. The light and dark red (green) shaded regions correspond to type-I and type-II classifications for positive (negative) curvature fluctuations, respectively.
• Figure 2: Initial configuration for three representative negative curvature fluctuations with amplitudes $\mu = -0.6$ (red), $-1$ (black), and $-1.6$ (green). Top panels: the initial curvature profile $\zeta(r)$, the areal radius ${R}(r)$, and the three-Ricci scalar ${}^{(3)}R(r)$. In the latter panel, positive values are represented with solid lines, whereas negative values with dashed line. Bottom panels: the corresponding non-linear compaction function $\mathcal{C}(r)$, its linear component, and the compaction's curvature $\kappa(r)$, computed assuming radiation domination ($\omega=1/3$). The chosen amplitudes exemplify the type-I (red), type-I/II transitional (black), and type-II (green) regimes. The vertical blue line in the bottom panels indicate the location of the maximum of $C_\ell$.
• Figure 3: Evolution of the density contrast $\rho_E/\rho_{\rm bkg}$(upper rows), relative recession velocity with respect the background (middle rows) and normalized Ricci Scalar by a factor $\mathfrak{a}(t)^2$ (bottom rows) for negative curvature fluctuations re-entering the Hubble horizon during radiation domination $(\omega = 1/3)$, obtained from numerical relativity simulations. Top panels: initial fluctuation with amplitude $\mu = -1.8$ and $\omega = 1/3$, which forms a PV that rebounds into a central overdensity and collapses into a PBH. Bottom panels: initial fluctuation with amplitude $\mu = -0.8$ and $\omega = 1/3$, which also forms a PV but whose rebound dissipates into sound waves. Underdensities are represented by a blue or purple colormaps, while overdensities by red or green colormaps. The yellow circle denotes the formation of an apparent horizon.
• Figure 4: Mass scaling of PBH formation for negative (left panel) and positive (right panel) curvature fluctuations.
• Figure 5: Formation and identification of the PBH's apparent horizon for $\mu= 0.8$ (top panels) and $\mu= -1.8$ (bottom panels) by using the $2M_{\rm MS}/R = 1$ (left panels) and the $\Theta_{+}<0$ conditions (right panels). The vertical dashed black line marks the location of the AH, shortly after its formation (depicted by red solid curves).