Probing Primordial Black Hole Formation from Domain Wall Isocurvature Perturbations: Constraints and Implications

TL;DR

This paper proposes a mechanism for primordial black hole formation from isocurvature perturbations induced by a domain-wall network that forms after discrete symmetry breaking. By modeling domain-wall evolution with the velocity-dependent one-scale (VOS) framework and computing Poisson-induced density fluctuations, the authors show that PBHs can form when the wall energy fraction reaches $f_w\sim0.1$ near domain-wall annihilation. They connect PBH production to the domain-wall-induced gravitational wave background that could explain nano-Hz PTA signals, performing a Bayesian analysis of NG15 and IPTA-DR2 data to constrain the annihilation temperature $T_{\rm ann}$ and wall fraction $f_w(T_{\rm ann})$, while accounting for the critical-collapse threshold with an effective equation of state. The key finding is that low domain-wall numbers, notably $N=1$ (and up to $N\sim2$), are excluded by PBH overproduction, while higher-$N$ scenarios (roughly $N\gtrsim6$) remain viable for some PTA interpretations; the work thus tightly links late-time domain-wall dynamics, PBH production, and stochastic gravitational waves in a testable cosmological framework.

Abstract

Domain walls are topological defects produced by the spontaneous symmetry-breaking of discrete symmetry during cosmological phase transitions. Domain walls can significantly contribute to the energy density in the late-evolution stage. We propose that the density perturbations from the fluctuations in the number density of the domain walls could collapse to form primordial black holes. This mechanism becomes effective when the domain wall energy density ratio to that of the radiation reaches about 0.1 in the radiation-dominated Universe. We find that models with $Z_2$ symmetry are excluded for interpreting pulsar timing array observations on the nano-Hz gravitational wave background since this model's domain wall number density fluctuations could lead to an overabundance of the primordial black holes. Moreover, the models, which generate approximately $N\sim 10$ domain walls from the spontaneous breaking of a discrete $Z_N$ symmetry, are also subject to stringent constraints due to the overproduction of primordial black holes.

Figures (12)

• Figure 1: Upper panel: The evolution of $\bar{L}$ (red curves) and $\bar{v}_w$ (blue curves) as a function of cosmic time $t/t_s$ in the VOS model is shown. The solid curves and the dot-dashed curves represent the results with a chopping parameter $c_w=0.81$ and $0.61$, respectively. Lower panel: The evolution of the closed domain wall, governed by Eq. \ref{['eq:SDW1']}, is illustrated for different initial radii, represented by red, green, and blue curves.
• Figure 2: Left: The variance $\sigma$ as a function of the PBH mass $M$. Right: The PBH relic abundance $\Omega_{\rm PBH}$ as a function of the PBH mass $M$. We take the wall number $N=1$.
• Figure 3: The solid curves represent the fit to the simulation results, denoted by the colored points, given in Ref. Musco:2012au with Eq. \ref{['eq:fit']}.
• Figure 4: Left: The critical density contrast $\delta_c$ as a function of the PBH mass $M$. Right: The PBH relic abundance $\Omega_{\rm PBH}$ as a function of the PBH mass $M$, assuming $N=1$ and a constant variance $\sigma^2=0.004$. The black lines represent the results with a constant $\delta_c$ in the radiation phase. The effects on $\delta_c$ and $\Omega_{\rm PBH}$ from the domain walls are represented by the blue and green curves for $\sigma_{w}^{1/3}=10^5$ GeV and $10^6$ GeV, respectively.
• Figure 5: The red (light red) and blue (light blue) regions represent the $1\sigma$ ($2\sigma$) regions of the 2D posterior distributions of the annihilation temperature $T_{\rm ann}$ and the domain wall density fraction $f_w(\rm ann)$ by fit to the NG15 and IPTA-DR2 datasets, respectively. The black dashed lines represent the $\Delta N_{\rm eff}$ constraints. The solid green line and dotted gray line represent contours of $\Omega_{\rm PBH}=10^{-3}$ and $0.25$ from the domain wall fluctuations, respectively.