Model dependence of the cosmological upper bound on the Higgs-boson mass

We consider an electroweak scenario for baryon asymmetry generation in an extended model with two Higgs doublets. The upper bound on the mass of the lightest Higgs boson is obtained. It is shown to coincide with that of the theory with one Higgs doublet, namely, $m_H<m_{\mathrm{cr}}\simeq 45$ GeV, if the masses of all Higgs bosons do not exceed the mass of the $W$ boson substantially. Otherwise the upper bound is shown still to exist but is greater than $m_{\mathrm{cr}}$ and depends on the actual values of the scalar-field self-coupling constants.