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

Abstract

Naïve 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.

v2: comment of cascades of large number of diagrams added. Clarification of why previous literature did not prove unitarity of the scalar sector. Comments on unitarity of the gauge sectors added and miscellaneous of clarifications. Accepted in PRD

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