Cosmology of Supercooled Universe

First-order phase transitions (FOPTs) are ubiquitous in physics beyond the Standard Model (SM). Recently, models with no dimensionful parameters in the tree-level action have been attracting much attention because they can predict a very strong FOPT with ultra-supercooling. In this paper, we study the cosmological signatures of such a supercooling model. As a concrete model, we consider the SM with two additional real scalars $\phi$ and $S$, which can realize the electroweak symmetry breaking via Coleman-Weinberg mechanism. One of the additional scalars $S$ can naturally become a Dark Matter (DM) candidate due to the $Z_2^{}$ symmetry of the action. We study the FOPT of this model and calculate the Gravitational Wave (GW) signals and the thermal relic abundance of $S$ taking the filtered effects into account. Within the envelope approximation, we find that the GW peak amplitude can reach $\sim 10^{-10}$ around the frequency $f\sim 10^{-3}~$Hz for model parameters $(v_\phi^{},\lambda_{\phi S}^{})\sim (200~{\rm TeV},1.6)$ where $v_\phi^{}$ is the vacuum expectation value of $\phi$ and $\lambda_{\phi S}^{}$ is the scalar mixing coupling. On the other hand, the filtered DM mechanism only works for $0.8\lesssim \lambda_{\phi S}^{}\lesssim 1$, where the GW peak amplitude is found to be quite small $\lesssim 10^{-17}$.