Primordial Black Hole Formation and Multimessenger Signals in a Complex Singlet Extension of the Standard Model

TL;DR

This work investigates PBH formation induced by a strongly first-order EWPT within the renormalizable Complex Singlet Extension of the Standard Model (CxSM), focusing on a degenerate-scalar scenario. It develops a quantitative framework connecting phase-transition dynamics to PBH abundance, and demonstrates that the same parameter space yields observable stochastic GWs and a sizeable Higgs triple-coupling deviation, enabling multimessenger tests with future gravitational-wave detectors and lepton colliders. PBH masses at formation are near $M_{\mathrm{PBH}}\sim10^{-5} M_\odot$, with the PBH fraction $f_{\mathrm{PBH}}$ highly sensitive to the Euclidean action via $S_3/T$ and to small shifts in model parameters; this region must also satisfy microlensing constraints. Overall, the study shows that PBH, GW, and collider observations can jointly probe the EWPT dynamics in a realistic Higgs-portal framework, offering a coherent path to test early-Universe physics at the electroweak scale.

Abstract

We investigate the formation of primordial black holes (PBHs) induced by a first-order electroweak phase transition in a realistic renormalizable framework, the complex singlet extension of the Standard Model. We perform a quantitative analysis of the PBH abundance and identify parameter regions consistent with current microlensing constraints. Furthermore, we show that the same parameter space predicts observable stochastic gravitational waves within the sensitivities of future space-based detectors, as well as a sizable deviation in the Higgs triple coupling that can be probed at future lepton colliders. Our results highlight a comprehensive multimessenger framework in which PBH, gravitational wave, and collider observations can jointly test the dynamics of a strongly first-order electroweak phase transition in the early Universe.

Figures (4)

• Figure 1: Parameter dependence of the PBH fraction in the $(\delta_2, d_2)$ plane. Here we take $v_S = 0.6~\mathrm{GeV}$ and $\theta = \pi/4$ as representative values to realize appropriate magnitudes of $\delta_2$ and $d_2$ in the degenerate scalar scenario. The red line represents the region where $10^{-4} \le f_{\mathrm{PBH}} \le 1$. The color map shows the Higgs triple coupling, which serves as an indicator of the EWPT strength.
• Figure 2: Temperature dependence of $S_3/T$, which characterizes the strength of the EWPT. The inset shows an enlarged view around the minimum of $S_3/T$.
• Figure 3: Predicted PBH abundance $f_{\mathrm{PBH}}$ as a function of the PBH mass normalized by the solar mass ($M_{\mathrm{PBH}}/M_{\odot}$). The gray shaded regions indicate existing microlensing constraints from Subaru HSC Niikura:2017zjd, OGLE Niikura:2019kqi, and EROS EROS-2:2006ryy. The red points correspond to the benchmark points BP2--BP5, while BP1 is not shown since its PBH fraction is too small to appear in the plot.
• Figure 4: The predicted GW spectra for the benchmark points BP1--BP5. The shaded regions indicate the sensitivity curves corresponding to $\mathrm{SNR} = 5$ of future space-based GW detectors, LISA Caprini:2015zloamaro2017laserCaprini:2019egz (red) and TianQin TianQin:2015yphHu:2018yqb (blue). GW signals above these curves are detectable with $\mathrm{SNR} > 5$.