Cosmological Signatures of the Conformal and Non-Conformal Next-to-Minimal Two-Higgs-Doublet Model

Abstract

We investigate cosmological signatures of the next-to-minimal two-Higgs-doublet model (N2HDM) in both the classically scale-invariant, or conformal, realization and in the corresponding non-conformal theory. Using a one-loop finite-temperature effective potential, collider and flavour constraints implemented through ScannerS, HiggsBounds and HiggsSignals, and a modified on-shell counterterm prescription for the conformal model, we identify parameter regions with a first-order electroweak phase transition and potentially observable stochastic gravitational waves. We find that both conformal and non-conformal scenarios can produce sound-wave signals in the sensitivity range of future space-based interferometers, including LISA, while the electroweak transitions complete promptly ($T_n\simeq T_p$), with pronounced supercooling below the critical temperature confined to the strongest transitions. The two scenarios nevertheless populate different regions of the scalar mass spectrum when the gravitational-wave signal is observable, suggesting that a future stochastic background measurement combined with collider information on the additional Higgs states could discriminate between the two realizations. We further study partonic Higgs-pair production, in the heavy-top approximation, and find that large deviations in the SM-like di-Higgs rate tend to occur away from the regions with the strongest gravitational-wave signals, while enhanced BSM Higgs-pair rates are mainly associated with the conformal model. The analysis highlights a complementary interplay between electroweak cosmology, scalar spectroscopy and Higgs self-interaction probes in extended Higgs sectors.