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

TL;DR

The paper investigates RG-improved Standard Model Higgs inflation with a large non-minimal curvature coupling $\xi$, showing that inflationary dynamics are governed by the running anomalous scaling $A_I(t)$ that flows to small negative values, realizing an asymptotic freedom-like behavior during inflation. By mapping electroweak-scale couplings to inflation-scale values and incorporating Goldstone contributions, the authors derive a Higgs-mass window $M_H \in [135.6, 184.5]$ GeV (for $M_t=171$ GeV) consistent with CMB observations, with the lower bound tied to vacuum stability and the upper bound to the observed $n_s$. The analysis emphasizes RG improvement and the role of gravity in regulating SM quantum corrections, discusses gauge/frame ambiguities, and proposes a gauge-invariant, spherical-coordinate formulation to stabilize the effective potential. The work also connects initial conditions for inflation to quantum cosmology (no-boundary/tunneling) and highlights the potential of $A_I(t)$-driven dynamics to underpin the early-universe inflationary scenario.

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.

Figures (7)

• Figure 1: Running $\lambda(t)$ for five values of the Higgs mass above the instability threshold. Dashed curves mark the boundaries of the inflation domain $t_{\rm end}\leq t\leq t_{\rm in}$.
• Figure 2: Running anomalous scaling for the critical Higgs mass (the red curve with a vertical segment at the singularity with $t_{\rm inst}\sim 41.6$) and for two masses in the stability domain (blue and green curves).
• Figure 3: The spectral index $n_s$ as a function of the Higgs mass $M_H$ for three values of the top quark mass.
• Figure 4: The Einstein frame effective potential for the instability threshold $M_H^{\rm inst}=134.27$ GeV. A false vacuum occurs at the instability scale $t_{\rm inst}\simeq 41.6$, $\varphi\sim 80 M_P$, which is much higher than the inflation scale $\varphi<\varphi_{\rm in}\simeq 0.04 M_P$. A hypothetical inflation domain (ruled out by the lower $n_s$ CMB bound and the requirement of the positive slope of $\hat{V}$ at $t\leq t_{\rm in}$) is marked by dashed lines.
• Figure 5: Inflaton potential at the lower CMB compatible value of $M_H$. A metastable vacuum exists at $t\simeq 42$ which is much higher than the inflation domain at the positive slope of the potential.