Black holes and gravitational waves from phase transitions in realistic models

Abstract

We study realistic models predicting primordial black hole (PBH) formation from density fluctuations generated in a first-order phase transition. We show that the second-order correction in the expansion of the bubble nucleation rate is necessary for accurate predictions and quantify its impact on the abundance of PBHs and gravitational waves (GWs). We find that the distribution of the fluctuations becomes more Gaussian as the second-order term increases. Consequently, models that predict the same PBH abundances can produce different GW spectra.

Figures (6)

• Figure 1: The distribution of $\delta$ at $k=0.9k_{\rm max}$ for benchmark points both giving roughly the observed PBH abundance in the asteroidal mass window if $T_{\rm reh} = 10^6\,$GeV.
• Figure 2: The color coding shows the PBH abundance generated in the phase transition and the thick solid contour highlights the contour for which $f_{\rm PBH} = 1$ if $T_{\rm reh} = 10^6\,$GeV. The dashed green and red contours show, respectively, the peak amplitudes of the primary and the secondary contributions to the present GW spectrum. The stars mark the points shown in Figs. \ref{['fig:Pkdelta']} and \ref{['fig:OmegaGW']}.
• Figure 3: The GW spectrum for the same benchmark points as in Fig. \ref{['fig:Pkdelta']} with $T_{\rm reh} = 10^6\,$GeV. The shaded regions in the right panel indicate the instantaneous sky averaged sensitivities of LISA, AEDGE and ET.
• Figure 4: Accuracy of the expansion of the decay rate for $v=3\times10^7$GeV and $g=0.33$ that gives $R_p H_p \approx 1$. The vertical lines show the nucleation time (left) and the percolation time (right).
• Figure 5: The purple and orange contours show the parameters $\beta/H_0$ and $\gamma/\beta$ defining the expansion of the nucleation rate up to second order (see Eq. \ref{['eq:Gamma']}) as a function of model parameters $v$ and $g$. The blue contours showing the PBH abundance are normalized to the observed DM abundance and the green contours show the mean PBH masses. The red region is excluded by BBN constraint on the reheating temperature after the transition and the grey region by the percolation criterion that matches the condition $R_p H_p < 1$.