Nearly Monochromatic Primordial Black Holes as total Dark Matter from Bubble Collapse

TL;DR

This work addresses forming primordial black holes (PBHs) as dark matter through bubble collapse during inflation without requiring an enhancement of small-scale curvature perturbations. It introduces a two-field model where the instanton field $\phi$ non-minimally couples to the inflaton $χ$ via a coupling $g(χ)$ that peaks at $χ=χ_*$, maximizing the false-vacuum–true-vacuum energy difference and the tunneling rate during inflation. By mapping the time-dependent tunneling rate to a PBH mass function, the authors show that both Coleman-De Luccia and Hawking-Moss tunneling produce a sharply peaked, nearly monochromatic PBH spectrum centered at a mass scale $M_*$; tuning $χ_*$ allows PBHs to account for all DM, or to populate sub-solar or supermassive regimes. The scenario does not inherently generate large induced gravitational waves, so a non-detection of IGWs would not rule out PBHs as DM, while the model remains testable via gravitational-wave and microlensing probes at specific mass ranges.

Abstract

We propose a two-field model where the inflaton $χ$ is non-minimally coupled to the instanton $φ$. By choosing an appropriate coupling function, we realize the scenario where the difference of the values of potential between false vacuum (FV) and true vacuum (TV) is maximized during inflation. Most of the bubbles are created at this time. After inflation ends, the potential value of FV drops below that of TV so that these bubbles collapse to form primordial black holes (PBHs). By tuning the parameters of our model, we analyze the Coleman-de Luccia (CDL) and Hawking-Moss (HM) process, finding that the corresponding mass function of PBHs is sharply peaked, implying that we can realize either PBHs as cold dark matter, sub-solar PBHs, or supermassive PBHs in this scenario without enhancement of primordial curvature perturbations.

Figures (4)

• Figure 1: Schematic illustration of the two dimensional potential $V(\chi,\phi)$. An inflaton starting from $\chi=\chi_i$ can either roll down along the blue trajectory all the time, or tunnel through the barrier and then roll down along the purple trajectory, resulting in bubble nucleation.
• Figure 2: Plots of $g(\chi)/g_0$ (top) and $V_\phi(\chi,\phi)$ (bottom) for \ref{['eq:g(chi)']}. During inflation, the value of $g(\chi)$ and thus the energy difference between FV and TV maximize at $\chi=\chi_*$, resulting in the highest tunneling rate. After inflation, $g(\chi<\chi_f)<0$ so that $V_\phi(\chi, \phi_-)<V_\phi(\chi, \phi_+)$, causing the collapse of the bubbles.
• Figure 3: Plot of $B_{\rm CDL}(\chi)$'s dependence on parameters $2g_0/\lambda$, $\lambda$ and $v$, where $\chi_*=4.66M_{\rm Pl}$ is fixed. [left] $\chi_0=0.3M_{\rm Pl}$, $\lambda=10^{4}$ and $v=10^{-4}M_{\rm Pl}$. [middle] $\chi_0=0.3M_{\rm Pl}$, $2g_0/\lambda=0.1$ and $v=10^{-4}M_{\rm Pl}$. [right] $\chi_0=0.3M_{\rm Pl}$, $2g_0/\lambda=0.02$ and $\lambda=10^{4}$. For a reasonable semi-classical bounce action, we keep $B_{\rm CDL}\gg1$.
• Figure 4: Mass function $f(M)$ of PBHs as DM from collapsing bubbles nucleated via CDL instanton, which stays consistent with current observational constraints Carr_2021. Evaporation constraints (red) show the extragalactic $\gamma$-ray background (EGB) Carr:2009jm. Lensing constraints (purple) come from microlensing by HSC, OGLE and Icarus event (I) Mroz:2024wiaEROS-2:2006ryy. Accretion constraints (light blue, yellow) come from X-ray binaries (XB) Inoue_2017 and CMB anisotropies measured by Planck (PA) Serpico:2020ehh. Dynamical constraints (green) are from infalling of halo objects due to dynamical friction (DF) and the CMB dipole (CMB) Carr:1997cn. Large-scale structure constraints (dark blue) demonstrate various cosmic structures (LSS) Carr_2018. The three curves of mass function $f(M)$ from left to right correspond to the choices for model parameters listed in Tab. \ref{['tab:parameter']}. The top axis relates the $\chi$ value of inflaton to the PBH mass $M$ through Eq. \ref{['eq:chi(M)']}.