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Standard Model Higgs boson mass from inflation

Fedor L. Bezrukov, Amaury Magnin, Mikhail Shaposhnikov

TL;DR

The paper shows that the Standard Model Higgs can act as the inflaton if it has a non-minimal coupling to gravity and the Higgs mass lies within a calculable window depending on the top mass, $m_{\min}<m_H<m_{\max}$. Using a renormalization-group–improved effective potential in the Einstein frame and solving one-loop RG equations in curved space, the authors find a robust inflationary prediction with $n_s\approx0.97$ and $r\approx0.0034$ that is largely independent of $m_H$ within the window; two renormalization prescriptions yield compatible results after RG running. The work links electroweak-scale physics to early-Universe inflation, offering testable implications for LHC measurements and potential beyond-SM extensions such as the nuMSM or scale-invariant cosmologies, and notes that higher-loop refinements are underway.

Abstract

We analyse one-loop radiative corrections to the inflationary potential in the theory, where inflation is driven by the Standard Model Higgs field. We show that inflation is possible provided the Higgs mass m_H lies in the interval m_min<m_H<m_max, where m_min=[136.7+(m_t-171.2)*1.95]GeV, m_max=[184.5+(m_t-171.2)*0.5]GeV and m_t is the mass of the top quark. Moreover, 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 correspondingly.

Standard Model Higgs boson mass from inflation

TL;DR

The paper shows that the Standard Model Higgs can act as the inflaton if it has a non-minimal coupling to gravity and the Higgs mass lies within a calculable window depending on the top mass, . Using a renormalization-group–improved effective potential in the Einstein frame and solving one-loop RG equations in curved space, the authors find a robust inflationary prediction with and that is largely independent of within the window; two renormalization prescriptions yield compatible results after RG running. The work links electroweak-scale physics to early-Universe inflation, offering testable implications for LHC measurements and potential beyond-SM extensions such as the nuMSM or scale-invariant cosmologies, and notes that higher-loop refinements are underway.

Abstract

We analyse one-loop radiative corrections to the inflationary potential in the theory, where inflation is driven by the Standard Model Higgs field. We show that inflation is possible provided the Higgs mass m_H lies in the interval m_min<m_H<m_max, where m_min=[136.7+(m_t-171.2)*1.95]GeV, m_max=[184.5+(m_t-171.2)*0.5]GeV and m_t is the mass of the top quark. Moreover, 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 correspondingly.

Paper Structure

This paper contains 5 sections, 17 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Inflation in tree approximation
  3. Renormalization group and effective potential
  4. Numerical results
  5. Conclusions

Figures (3)

  • Figure 1: Non-minimal coupling parameter $\xi$ as a function of the Higgs mass $m_H$. Solid line is for the choice I, dashed---for the choice II.
  • Figure 2: RG improved effective potential. The four nearly coinciding upper lines correspond to the choice I and $m_H=\unit[137,140,170]{GeV}$ and choice II with $m_H=\unit[170]{GeV}$. The middle and lower lines correspond to the choice II with $m_H=\unit[140]{GeV}$ and $\unit[137]{GeV}$, respectively.
  • Figure 3: Spectral index $n_s$ depending on the Higgs mass $m_H$. Solid line is for the choice I, dashed---for the choice II.