Supercooled Phase Transitions with Radiative Symmetry Breaking

Abstract

First-order phase transitions produce gravitational waves and primordial black holes. They always occur in field theories where symmetries are radiatively broken and masses are correspondingly generated. These theories predict a period of supercooling: phase transitions become effective at temperatures much smaller than the symmetry-breaking scale. This paper reviews a model-independent approach to study phase transitions in this scenario, which can be adopted if supercooling is strong enough. Perturbative methods can be used to determine the effective action and such model-independent approach allows us to obtain ready-to-use formulas that can be applied to any specific model of this sort.

Figures (4)

• Figure 1: A qualitative picture of the temperature-dependent effective potential corresponding to a FOPT: the two minima associated with the two phases are separated by a potential barrier; $T_c$ is the critical temperature. Figure reproduced from Ref. Salvio:2023qgb.
• Figure 2: The time-independent bounce and the corresponding integrand function (divided by $8\pi$) appearing in the bounce action, Eq. (\ref{['bounceSd']}), for the effective potential $\overline V_{\rm eff}(\chi) = \frac{m^2}{2} \chi^2-\frac{\lambda}{4}\chi^4$ of the supercool expansion at LO and setting $\lambda=1$. Figure reproduced from Ref. Salvio:2023qgb.
• Figure 3: The relevant bounce and the corresponding integrand function (divided by $8\pi L \xi^2$) appearing in the bounce action in (\ref{['S3improS']}) for the effective potential (\ref{['barVnlo']}) and varying $\tilde{\lambda}\equiv \lambda m^2/k^2$. The maximal height of the curves increases by decreasing $\tilde{\lambda}$.
• Figure 4: The solution $\tilde{\lambda}_n$ of Eq. (\ref{['lteq']}) as a function of $a_1$ and $a_2$ defined in (\ref{['a1a2']}). The inset in the right plot gives the maximal value of $a_2$ for a given $a_1$ such that the solution $\tilde{\lambda}_n$ exists. Using the definitions of $\tilde{\lambda}$ and $\lambda$ in (\ref{['deflambdat']}) and (\ref{['mlambdaDef']}) one can extract the nucleation temperature. Figure reproduced from Ref. Salvio:2023ext.