Standard Model Higgs boson mass from inflation: two loop analysis

TL;DR

This work extends Higgs-inflation analysis by incorporating two-loop radiative corrections to the effective potential within the Standard Model with a large non-minimal coupling to gravity. It shows that the inflationary predictions, particularly the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$, depend on the renormalization prescription, with prescription I yielding $n_s\approx0.97$ and $r\approx0.0034$ largely independent of $m_H$, while prescription II introduces $m_H$-dependent variations. The two-loop RG running shifts the viable Higgs-mass window but preserves the overall mechanism that the SM can drive inflation without new physics up to the Planck scale. The results highlight intrinsic theoretical uncertainties tied to renormalization schemes and frame choices, underscoring that precise cosmological measurements and precise SM parameters are needed to fix Planck-scale physics.

Abstract

We extend the analysis of \cite{Bezrukov:2008ej} of the Standard Model Higgs inflation accounting for two-loop radiative corrections to the effective potential. As was expected, higher loop effects result in some modification of the interval for allowed Higgs masses m_min<m_H<m_max, which somewhat exceeds the region in which the Standard Model can be considered as a viable effective field theory all the way up to the Planck scale. The dependence of the index n_s of scalar perturbations on the Higgs mass is computed in two different renormalization procedures, associated with the Einstein (I) and Jordan (II) frames. In the procedure I the predictions of the spectral index of scalar fluctuations and of the tensor-to-scalar ratio practically do not depend on the Higgs mass within the admitted region and are equal to n_s=0.97 and r=0.0034 respectively. In the procedure II the index n_s acquires the visible dependence on the Higgs mass and and goes out of the admitted interval at m_H below m_min. We compare our findings with the results of \cite{DeSimone:2008ei}.