Beyond dimensional analysis: Higgs and new Higgs inflations do not violate unitarity

Naive dimensional analysis seems to suggest possible unitarity violations in the framework of the Higgs and new Higgs inflationary scenarios. These violations seem to happen around the value in which the potential energy, per a given Higgs boson's vacuum expectation value, crosses the perturbative cutoff scale calculated around the electroweak vacuum. Conversely to these expectations, we show that, by using an exact analysis of the background dependent cutoff scale, and by including the contribution of the phase-space volume in the perturbative scattering amplitudes of scalars, no violation of (perturbative) unitarity might ever happen during the whole Universe evolution.