Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Higgs mass range from Standard Model false vacuum Inflation in scalar-tensor gravity

Isabella Masina, Alessio Notari

TL;DR

This paper proposes that a shallow high-scale false minimum in the Standard Model Higgs potential can drive cosmological inflation if gravity is augmented by a scalar-tensor sector (Brans-Dicke-like field). By analyzing the Einstein-frame dynamics, slow-roll parameters, and the connection between perturbation amplitudes and the false minimum, the authors derive a narrow prediction for the Higgs mass, m_H ≈ 126 GeV, consistent with current collider bounds and precision fits. The model yields testable predictions for the scalar spectral index n_S and the tensor-to-scalar ratio r, and remains viable across a class of higher-order gravitational couplings, with the exit from inflation achieved through bubble nucleation and percolation followed by reheating. If the Higgs mass is confirmed in this window, it would provide a striking link between electroweak-scale physics and the early universe, potentially supporting Higgs-driven inflation in a scalar-tensor gravity framework.

Abstract

If the Standard Model is valid up to very high energies it is known that the Higgs potential can develop a local minimum at field values around $10^{15}-10^{17}$ GeV, for a narrow band of values of the top quark and Higgs masses. We show that in a scalar-tensor theory of gravity such Higgs false vacuum can give rise to viable inflation if the potential barrier is very shallow, allowing for tunneling and relaxation into the electroweak scale true vacuum. The amplitude of cosmological density perturbations from inflation is directly linked to the value of the Higgs potential at the false minimum. Requiring the top quark mass, the amplitude and spectral index of density perturbations to be compatible with observations, selects a narrow range of values for the Higgs mass, $m_H=126.0\pm 3.5$ GeV, where the error is mostly due to the theoretical uncertainty of the 2-loop RGE. This prediction could be soon tested at the Large Hadron Collider. Our inflationary scenario could also be further checked by better constraining the spectral index and the tensor-to-scalar ratio.

The Higgs mass range from Standard Model false vacuum Inflation in scalar-tensor gravity

TL;DR

This paper proposes that a shallow high-scale false minimum in the Standard Model Higgs potential can drive cosmological inflation if gravity is augmented by a scalar-tensor sector (Brans-Dicke-like field). By analyzing the Einstein-frame dynamics, slow-roll parameters, and the connection between perturbation amplitudes and the false minimum, the authors derive a narrow prediction for the Higgs mass, m_H ≈ 126 GeV, consistent with current collider bounds and precision fits. The model yields testable predictions for the scalar spectral index n_S and the tensor-to-scalar ratio r, and remains viable across a class of higher-order gravitational couplings, with the exit from inflation achieved through bubble nucleation and percolation followed by reheating. If the Higgs mass is confirmed in this window, it would provide a striking link between electroweak-scale physics and the early universe, potentially supporting Higgs-driven inflation in a scalar-tensor gravity framework.

Abstract

If the Standard Model is valid up to very high energies it is known that the Higgs potential can develop a local minimum at field values around GeV, for a narrow band of values of the top quark and Higgs masses. We show that in a scalar-tensor theory of gravity such Higgs false vacuum can give rise to viable inflation if the potential barrier is very shallow, allowing for tunneling and relaxation into the electroweak scale true vacuum. The amplitude of cosmological density perturbations from inflation is directly linked to the value of the Higgs potential at the false minimum. Requiring the top quark mass, the amplitude and spectral index of density perturbations to be compatible with observations, selects a narrow range of values for the Higgs mass, GeV, where the error is mostly due to the theoretical uncertainty of the 2-loop RGE. This prediction could be soon tested at the Large Hadron Collider. Our inflationary scenario could also be further checked by better constraining the spectral index and the tensor-to-scalar ratio.

Paper Structure

This paper contains 13 sections, 41 equations, 8 figures.

Table of Contents

  1. Introduction
  2. The inflationary model
  3. Slow-roll parameters and the number of e-folds
  4. Tensor to scalar ratio and scalar spectral index
  5. Amplitude of perturbations and Higgs potential at the false minimum
  6. Finding a viable minimum
  7. The Higgs mass range
  8. Post-Tunneling evolution
  9. Further issues
  10. Exponential inflation with quadratic and higher oder terms
  11. Effect of $\beta$
  12. Higher order terms
  13. Conclusions

Figures (8)

  • Figure 1: Left: dependence of $n_S$ on $\gamma$ when $0\le \beta \lesssim 5 \times 10^{-4}$. The curves are obtained for the representative values of $\bar{N}=40,50,60$. Right: dashed curves display $r$ as a function of $n_S$ for selected values of $\gamma$ (and taking $\beta=0$). The narrow shaded (green) region is found by requiring $\bar{N} \approx 50 \pm 10$. The larger shaded (red) regions are to the $1$ and $2\sigma$ ranges allowed experimentally for $r$ and $n_S$Komatsu:2010fb.
  • Figure 2: Value of the Higgs potential at the false minimum as a function of $\gamma$ and for $40\le \bar{N} \le 60$. The shaded region shows that the range selected by our inflationary model is $10^{-3.4} \le V(\chi_0)^{1/4}/M\le 10^{-2.2}$.
  • Figure 3: Higgs potential as a function of the Higgs field value $\chi$. We fixed $m_t=171.8$ GeV and, from top to bottom, $m_H=125.2,125.158,125.157663$ GeV. We also fixed $\alpha_3(m_Z)=0.1184$. The shaded region is the range selected by our inflationary model: $10^{-3.4} \le V(\chi_0)^{1/4}/M\le 10^{-2.2}$. The right panel is a magnification of the false vacuum region.
  • Figure 4: The (cyan) solid segments indicate the $m_t-m_H$ values compatible with a Higgs false minimum potential consistent with the requirement from inflation, fig.\ref{['fig-Vmin']}. The three segments show the uncertainty associated with $\alpha_3(m_Z)=0.1184 \pm 0.0007$ at $1\sigma$ (PDG 2011). The shaded horizontal bands are the $1\sigma$ and $2 \sigma$ ranges for $m_t$ from the GFitter analysis GFitter. The central (blue) spot represents the region compatible with both SM false vacuum inflation and the experimental range of $m_t$: this selects the narrow range $m_H=126.0\pm 3.5$ GeV, as pictorially represented via the arrow. The outer vertical shaded regions are the $m_H$ exclusion regions from direct searches at LEP, LHC and Tevatron. The central (yellow) vertical region with $m_H=124-127$ GeV is the region of the LHC excess of events. Dashed lines mark the values corresponding to the transition between stability, metastability and instability.
  • Figure 5: Analytical calculation of $n_S$ and $r$ as a function of $\beta$ for $n=4$. Values of $\gamma_4$ and $\bar{N}$ are indicated in the plots.
  • ...and 3 more figures