Asymptotic freedom in inflationary cosmology with a non-minimally coupled Higgs field

TL;DR

This paper investigates how a non-minimally coupled Higgs field can serve as an inflaton, revealing asymptotic freedom and specific parameter ranges consistent with CMB data, with implications for early universe conditions.

Contribution

It demonstrates asymptotic freedom in Higgs inflation with non-minimal coupling and identifies the Higgs mass range compatible with observational data and theoretical bounds.

Findings

Higgs mass range 135.6-184.5 GeV compatible with CMB data

Asymptotic freedom occurs except at boundary values

The anomalous scaling A_I becomes small and negative at inflation scale

Abstract

We consider the renormalization group improvement in the theory of the Standard Model Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. It suggests the range of the Higgs mass $135.6 {\rm GeV} \lesssim M_H\lesssim 184.5 {\rm GeV}$ compatible with the current CMB data (the lower WMAP bound on $n_s$), which is close to the widely accepted range dictated by the electroweak vacuum stability and perturbation theory bounds. We find the phenomenon of asymptotic freedom induced by this non-minimal curvature coupling, which brings the theory to the weak coupling domain everywhere except at the lower and upper boundary of this range. The renormalization group running of the basic quantity ${\boldmath $A_I$}$ -- the anomalous scaling in the non-minimally coupled Standard Model, which analytically determines all characteristics of the CMB spectrum -- brings ${\boldmath $A_I$}$ to small negative values at the inflation scale. This property is crucial for the above results and may also underlie the formation of initial conditions for the inflationary dynamics in quantum cosmology.