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

TL;DR

This paper demonstrates that, contrary to naive expectations, Higgs and new Higgs inflation models do not violate unitarity when considering an exact background-dependent cut-off and phase-space contributions, ensuring consistency throughout cosmic evolution.

Contribution

The study provides an exact analysis of the background-dependent cut-off scale and includes phase-space effects, showing no unitarity violation in Higgs inflation scenarios.

Findings

No unitarity violation during cosmic evolution

Exact background-dependent cut-off analysis used

Phase-space contributions are crucial for unitarity

Abstract

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.