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In the first scenario, we revise the upper bound of the cutoff scale of thedimension-six potential Higgs operator required for a successful electroweakbaryogenesis in the case of a modified expansion history caused by theexistence of a non-interacting scalar field at the time phase transitionhappens. The upper bound 860 GeV of the cutoff scale in the conventional casecan be improved to 1 TeV in the modified expansion case under certainconditions. In the second scenario, we consider the Randall-Sundrum type IImodel. We show that the lower bound of the five-dimensional Planck scale inthis model, which is determined from the validity of Newtonian gravitationalpotential at small distance, turns out to be crucial in eliminating this modelas a viable candidate to satisfy the sphaleron bound; however, again modifyingthe expansion history by including a non-interacting scalar field at theelectroweak scale can then make this model satisfy the sphaleron bound with acertain parameter space.

Sphaleron bound in some nonstandard cosmology scenarios