Phenomenology of bubble size distributions in a first-order phase transition

TL;DR

This work investigates how non-monochromatic FV/TV bubble radii in a cosmological dark-sector first-order phase transition produce extended FB and PBH mass distributions and how these extend observational signatures. The authors derive TV/FV bubble-radius distributions at percolation, map them to FB/PBH mass spectra, and assess their impact on gravitational waves by convolving the DBPL GW template with the radius distribution. They also analyze gravitational microlensing signals for FBs and PBHs and the extragalactic gamma-ray spectrum from PBH Hawking evaporation, finding distinctive features such as a shift/broadening in the GW peak and a mild 5–10 MeV break in the gamma-ray spectrum for extended distributions. The results show that extended mass distributions enlarge the FOPT parameter space accessible to microlensing and gamma-ray observations, offering new avenues (e.g., AMEGO-X/e-ASTROGAM, Subaru-HSC, THEIA/muAres) to test dark FOPT scenarios and distinguish them from monochromatic hypotheses.

Abstract

In a cosmological first-order phase transition (FOPT), the true and false vacuum bubble radius distributions are not expected to be monochromatic, as is usually assumed. Consequently, Fermi balls (FBs) and primordial black holes (PBHs) produced in a dark FOPT will have extended mass distributions. We show how gravitational wave (GW), microlensing and Hawking evaporation signals for extended bubble radius/mass distributions deviate from the case of monochromatic distributions. The peak of the GW spectrum is shifted to lower frequencies, and the spectrum is broadened at frequencies below the peak frequency. Thus, the radius distribution of true vacuum bubbles introduces another uncertainty in the evaluation of the GW spectrum from a FOPT. The extragalactic gamma-ray signal at AMEGO-X/e-ASTROGAM from PBH evaporation may evince a break in the power-law spectrum between 5 MeV and 10 MeV for an extended PBH mass distribution. Optical microlensing surveys may observe PBH mass distributions with average masses below $10^{-10} M_\odot$, which is not possible for monochromatic mass distributions. This expands the FOPT parameter space that can be explored with microlensing.

Figures (7)

• Figure 1: Comparison between the FV and TV radius distributions in Eq. (\ref{['eq:x']}).
• Figure 2: The extended mass distributions (at PBH production) for the benchmark points in Table \ref{['table1']}. The crosses mark the average mass; the pluses mark the corresponding monochromatic mass.
• Figure 3: The solid curves are the GW spectra for the benchmark points in Table \ref{['table1']} for extended bubble radius distributions. The dashed and dotted curves show the corresponding spectra for monochromatic radius distributions, evaluated at $\langle R \rangle_\star$ (Eq. \ref{['rstar']}) and $R_\star$ (Eq. \ref{['eq:Rmono']}), respectively.
• Figure 4: The parameter space excluded at 95% C.L. by Subaru-HSC's microlensing survey with 7 hours of observation is shown in yellow, and the expected 95% C.L. sensitivity with 70 hours of observation is shown in red. In the green regions, the FOPT generates GWs that are detectable by THEIA/$\mu$Ares. The upper row is for extended mass distributions and the lower row is for monochromatic distributions. $\langle M_{\rm FB} \rangle$ and $\langle R_{\rm FB} \rangle$ denote the average FB mass and radius, respectively.
• Figure 5: The same as Fig. \ref{['fig:FB_microlensing']}, but for microlensing by PBHs.