From inflation to cosmological electroweak phase transition with a complex scalar singlet

In this work, we investigate the possibility to realize inflation and strong first order electroweak phase transitions(SFOEWPT) together with the relic density explanation. We studied the usual Higgs-portal real singlet dark matter model and the global U(1) breaking complex singlet model with the pseudoscalar being dark matter candidate. We focus on higher dark matter parameter regions due to the lower dark matter masses region are almost excluded by the current direct detection experiments except that of the so-called ${\it Higgs~ funnel ~regime}$ with $m_{DM}\sim m_h/2$. In both models, the SFOEWPT can occur through two-step where the magnitude of the Higgs-singlet quartic couplings can account for the Higgs or singlet inflation. The usual Higgs-portal real singlet dark matter model can not address the correct relic density together with the explanation of inflation and SFOEWPT. With the complex singlet model, the correct relic density can also be obtained simultaneously when the mixing angle $0.1<\theta<0.2$ and the dark matter mass is $\sim800$ GeV.