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Formation of primordial black holes through Q-balls

Shinta Kasuya, Masahiro Kawasaki, Alexander Kusenko, Shunsuke Neda

TL;DR

Can Q-ball density perturbations seed primordial black holes in the early universe? The authors develop a formalism to compute density perturbations from arbitrary Q-ball charge distributions and show the sub-horizon PBH formation rate in a matter-dominated era matches the familiar super-horizon result. They apply the method to gauge-mediated SUSY-breaking Q-balls with lattice-derived charge spectra, showing that the resulting density perturbations can generate PBHs in the mass range $M\sim 10^{-15}\,M_\odot$ to $5\times10^{-12}\,M_\odot$, potentially explaining all dark matter. They further connect the PBH mass scale to the SUSY-breaking scale, $M_F\sim 10^6$ GeV, and discuss the required conditions, constraints, and implications for SUSY phenomenology and cosmology.

Abstract

We study the primordial black hole (PBH) formation from Q-balls that are non-topological solitons in scalar field theories. We develop a formula for calculating the density perturbations from the Q-ball charge distribution. We also re-examine the condition for the PBH formation in the matter-dominated era and show that the previously derived formula for super-horizon density fluctuations can be applied to the sub-horizon density perturbations. As an example, we consider the Q-balls in the case of gauge-mediated supersymmetry (SUSY) breaking, whose charge distribution was obtained by the lattice simulation. We find that the density perturbations are large enough to produce a significant number of PBHs with mass $10^{-15}\,M_\odot -5\times 10^{-12}\, M_\odot$, which can explain all the dark matter in the universe. In the context of supersymmetry, this mass range corresponds to the SUSY breaking scale $\sim 10^6$ GeV, which is consistent with the SUSY particle masses $\sim 10$ TeV.

Formation of primordial black holes through Q-balls

TL;DR

Can Q-ball density perturbations seed primordial black holes in the early universe? The authors develop a formalism to compute density perturbations from arbitrary Q-ball charge distributions and show the sub-horizon PBH formation rate in a matter-dominated era matches the familiar super-horizon result. They apply the method to gauge-mediated SUSY-breaking Q-balls with lattice-derived charge spectra, showing that the resulting density perturbations can generate PBHs in the mass range to , potentially explaining all dark matter. They further connect the PBH mass scale to the SUSY-breaking scale, GeV, and discuss the required conditions, constraints, and implications for SUSY phenomenology and cosmology.

Abstract

We study the primordial black hole (PBH) formation from Q-balls that are non-topological solitons in scalar field theories. We develop a formula for calculating the density perturbations from the Q-ball charge distribution. We also re-examine the condition for the PBH formation in the matter-dominated era and show that the previously derived formula for super-horizon density fluctuations can be applied to the sub-horizon density perturbations. As an example, we consider the Q-balls in the case of gauge-mediated supersymmetry (SUSY) breaking, whose charge distribution was obtained by the lattice simulation. We find that the density perturbations are large enough to produce a significant number of PBHs with mass , which can explain all the dark matter in the universe. In the context of supersymmetry, this mass range corresponds to the SUSY breaking scale GeV, which is consistent with the SUSY particle masses TeV.

Paper Structure

This paper contains 7 sections, 74 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Density perturbations of Q-balls
  3. PBH formation by sub-horizon fluctuations
  4. PBH formation by Q-balls
  5. Constraints on PBH formation
  6. Q-balls in supersymmetric models
  7. Summary and Discussion

Figures (3)

  • Figure 1: The PBH fraction for $\sigma_{Q,H}=3.4\times 10^{-3}$. The solid, dashed, and dot-dashed lines are for ($m_\mathrm{eff}/\mathrm{MeV}$, $T_\mathrm{dec}/\mathrm{GeV}$) = ($0.01, 10^4)$, $(1, 10^4)$, and $(0.01, 10^2)$, respectively.
  • Figure 2: The PBH fraction for $\sigma_{Q,H}=3.4\times 10^{-3},~T_\mathrm{dec}=2 \times 10^4\mathrm{GeV}$, $m_{\mathrm{eff}}=0.01\mathrm{MeV}$. The shaded regions show the observational constrains from $\gamma$-rays Carr:2009jm, microlensing(HSC Niikura:2017zjd, OGLE Niikura:2019kqi, EROS EROS-2:2006ryy), and CMB Serpico:2020ehh.
  • Figure 3: Constraints on $\Omega_\mathrm{PBH}/\Omega_\mathrm{DM}$. The blue region is excluded from the constraint \ref{['eq:const1']} while the red region is excluded from \ref{['eq:const2']}. The green region is excluded from the miclolensing observation by HSC Niikura:2017zjd.