Supercooling exit from charge supersaturation

TL;DR

Baratella shows that eternal supercooling in a quasi scale invariant scalar sector can be escaped if the system carries a conserved charge and develops a nonzero chemical potential $μ$. By relating $μ$ to the fixed entropy-to-charge ratio $S/Q$ and deriving a condensation criterion $q_φ μ > \\sqrt{a}\,T$, the paper identifies a dimensionless parameter $κ = 3 g Q/(q_φ^2 \\sqrt{a} S)$ that can cross unity during cosmic cooling, thereby triggering a Bose–Einstein condensation that ends the false vacuum phase. The work provides explicit expressions for the leading thermal masses from scalar quartics, Yukawa couplings, and gauge interactions, and demonstrates the mechanism across three classes of examples: scalar decoupling, charged fermion multiplets, and a dynamically generated exit scale (including a QCD-like confinement scenario). These results illustrate a robust, non-tunneling route to the true vacuum with implications for inflationary cosmology and the behavior of hidden sectors. The approach emphasizes the interplay between temperature, particle content, and charge distribution in determining phase transitions in the early universe.

Abstract

Systems that feature a scalar field $φ$ with a quasi scale invariant potential, metastable at $φ=0$, can remain trapped, during cosmic evolution, in the `wrong' vacuum because the process of bubble nucleation to the true vacuum is inefficient. If $φ$ carries a conserved charge $Q$, the presence in the system of a non-zero chemical potential for $Q$ offers the possibility of escaping eternal supercooling: when a species decouples from the plasma the balance among the stabilising effect of temperature and the destabilising effect of chemical potential can change in favour of the latter, so that $φ$ condenses and triggers the transition to the stable phase.

Figures (2)

• Figure 1: Contours of $\kappa$, defined in (\ref{['master']}), at fixed entropy $S$ and charge $Q$, as a function of the number of active species $g$ and the ratio of the scalar's thermal mass to temperature $\beta m_\phi=\sqrt a$ (schematic). Both $g$ and $\sqrt a$ are approximately piecewise constant functions of $T$ that decrease under cooling when $T$ crosses a physical scale $\Lambda$. The change in these two parameters can be such that the system goes from the yellow region ($\kappa<1$) to the blue region ($\kappa>1$) where a condensate is formed. The contours of $\kappa$ can also be thought of as different critical lines ($\kappa=0$) at varying $Q$ or $S$.
• Figure 2: The one-loop self energy of $\phi$ in the model specified by (\ref{['Yukawa']}) comes from the above diagram. Including thermal effects amounts to compute it with thermal instead of vacuum propagators for $\psi$ and $\chi$.