Cosmology of Supercooled Universe

Abstract

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 $\varphi$ 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 $(v_{\varphi }^{},{\lambda }_{\varphi S}^{})\sim (200\mathrm{TeV},1.6)$ where $v_{\varphi }^{}$ is the vacuum expectation value of $\varphi$ and ${\lambda }_{\varphi S}^{}$ is the scalar mixing coupling. On the other hand, the filtered DM mechanism only works for $0.8\lesssim {\lambda }_{\varphi S}^{}\lesssim 1$, where the GW peak amplitude is found to be quite small $\lesssim 10^{-17}$.

Published version in PRD, 26 pages, 6 figures

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