Beyond dimensional analysis: Higgs and new Higgs inflations {\it do not} violate unitarity

Understand

Na\"ive 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 given Higgs boson's vacuum expectation value, crosses the perturbative cut-off scale calculated around the electroweak vacuum.
• Conversely to these expectations, in this paper we show that, by using an exact analysis of the background dependent cut-off scale, and by including the contribution of the phase-space volume in the perturbative scattering amplitudes, no violation of (perturbative) unitarity might ever happen during the whole Universe evolution.