New Model of Inflation with Non-minimal Derivative Coupling of Standard Model Higgs Boson to Gravity

TL;DR

The paper confronts the problem of realizing Higgs-driven inflation within the Standard Model. It shows that minimal Higgs–gravity coupling cannot sustain slow-roll inflation without conflicting with quantum gravity bounds, and that non-minimal scalar–gravity couplings to reduce the inflationary scale face unitarity issues. It then introduces a unique non-minimal derivative coupling to gravity, $S=\int d^4x\sqrt{-g}[\frac{R}{2\kappa^2}-\frac{1}{2}(g^{\mu\nu}-w^2 G^{\mu\nu})\partial_\mu\Phi\partial_\nu\Phi-\frac{\lambda}{4}\Phi^4]$, which propagates no extra DOF and can yield slow-roll inflation with SM Higgs parameters while remaining unitary during inflation, with the effective self-coupling suppressed as $\lambdā \sim \lambda/(w^4 H^4)$. The model yields viable inflation for suitable $w$ (e.g., $w/\kappa$ of order $10^2$ and $r=\Phi_M/\Phi_i \sim 10^4$), and radiative corrections are argued to be subleading, preserving the flatness of the potential. This provides a Higgs-driven inflation scenario compatible with current data and without introducing new degrees of freedom or unitarity violations.

Abstract

In this letter we show that there is a unique non-minimal derivative coupling of the Standard Model Higgs boson to gravity such that: it propagates no more degrees of freedom than General Relativity sourced by a scalar field, reproduces a successful inflating background within the Standard Model Higgs parameters and, finally, does not suffer from dangerous quantum corrections.