Q-balls from thermal balls during a first-order phase transition: a numerical study

Abstract

We numerically study the Q-ball formation triggered by a cosmological first-order phase transition within the Friedberg-Lee-Sirlin model. By performing lattice simulations, we track the nonequilibrium dynamics throughout the transition, providing a precise description of the Q-ball formation mechanism and the resulting mass spectrum. Collapsing false-vacuum regions first form thermal balls, which subsequently cool via dissipative interactions and stabilize into long-lived Q-balls with nonzero spin. We observe a large population of low-mass Q-balls, as well as rare, massive Q-balls that are several times larger than the analytical prediction. The final Q-ball population exhibits a broad mass spectrum spanning over two orders of magnitude, characterized by an exponential tail of number density at large masses. The simulations suggest that the Q-ball abundance is approximately $50\%$ higher than predicted by analytical estimates, adjusting the result in the context of Q-balls as dark matter candidates.

Figures (5)

• Figure 1: Formation, cooling, and stabilization of a single Q-ball from a collapsing false-vacuum bubble.
• Figure 2: Time evolution of the effective radius of the central false-vacuum region. The rapid initial decrease corresponds to the contraction of the false vacuum and the formation of a thermal ball, followed by a cooling phase and the eventual emergence of a stable Q-ball.
• Figure 3: Isosurface visualization of Q-balls at the final simulation time $t=1000\,\omega_*^{-1}$ in a representative realization. Blue regions indicate domains with $\phi<\phi_{\mathrm{b}}/2$, corresponding to the interiors of individual Q-balls.
• Figure 4: Histogram of the Q-ball mass. Curves with colors ranging from light to dark correspond to time slices from $t=100\,\omega_*^{-1}$ to $t=1000\,\omega_*^{-1}$ with a time interval $\delta t=100\,\omega_*^{-1}$. The black dashed curve shows the exponential fit given in Eq. (\ref{['eq:exp']}).A light-blue dash-dotted line marks the analytically predicted characteristic Q-ball mass,$\tilde{M}_*=173.8$, in our benchmark model.
• Figure 5: Time evolution of the Q-ball mass-fraction distribution $Mp(M)$. Curves with colors ranging from light to dark correspond to time slices from early to late times. The blue dash--dotted line marks the analytically predicted characteristic Q-ball mass.