Standard Model with a real singlet scalar and inflation

We study the post-inflationary dynamics of the Standard Model Higgs and a real singlet scalar $s$, coupled together through a renormalizable coupling $\lambda_{sh}h^2s^2$, in a $Z_2$ symmetric model that may explain the observed dark matter abundance and/or the origin of baryon asymmetry. The initial values for the Higgs and $s$ condensates are given by inflationary fluctuations, and we follow their dissipation and relaxation to the low energy vacua. We find that both the lowest order perturbative and the non-perturbative decays are blocked by thermal effects and large background fields and that the condensates decay by two-loop thermal effects. Assuming instant reheating at $T=10^{16}$ GeV, the characteristic temperature for the Higgs condensate thermalization is found to be $T_h \sim 10^{14}$ GeV, whereas $s$ thermalizes typically around $T_s \sim 10^{6}$ GeV. By that time, the amplitude of the singlet is driven very close to the vacuum value by the expansion of the universe, unless the portal coupling takes a value $\lambda_{sh}\lesssim 10^{-7}$ and the singlet $s$ never thermalizes. With these values of the coupling, it is possible to slowly produce a sizeable fraction of the observed dark matter abundance via singlet condensate fragmentation and thermal Higgs scattering. Physics also below the electroweak scale can therefore be affected by the non-vacuum initial conditions generated by inflation.