Higgs inflation at the critical point

TL;DR

This paper studies Higgs inflation with a non-minimal coupling to gravity and shows that radiative corrections impose a critical Higgs mass $M_{\text{crit}}$ for self-consistent inflation. Away from the critical point the inflationary indices are nearly universal ($n_s \approx 0.97$, $r \approx 0.003$), but near the critical point they depend sensitively on high-energy inflationary masses $m_t^*$ and $M_h^*$, potentially yielding much larger $r$. By treating $\kappa$, $\lambda_0$, and $\xi$ as independent at the inflation scale and mapping low-energy inputs to high-energy parameters via RG running and jumps in couplings at $h^* = \frac{M_P}{2\sqrt{6}\,\xi}$, the paper provides explicit formulas for $\lambda_0$, $q$, $b$ as functions of $M_h^*$ and $m_t^*$, linking cosmology to SM parameters. The results imply that a measured large $r$ would constrain $m_t^*$ and $M_h^*$ to lie near their experimental values and illustrate how cosmological data can inform the high-energy behavior of the SM, assuming validity up to the Planck scale.

Abstract

Higgs inflation can occur if the Standard Model (SM) is a self-consistent effective field theory up to inflationary scale. This leads to a lower bound on the Higgs boson mass, $M_h \geq M_{\text{crit}}$. If $M_h$ is more than a few hundreds of MeV above the critical value, the Higgs inflation predicts the universal values of inflationary indexes, $r\simeq 0.003$ and $n_s\simeq 0.97$, independently on the Standard Model parameters. We show that in the vicinity of the critical point $M_{\text{crit}}$ the inflationary indexes acquire an essential dependence on the mass of the top quark $m_t$ and $M_h$. In particular, the amplitude of the gravitational waves can exceed considerably the universal value.

Figures (8)

• Figure 1: The schematic change of the form of the effective potential depending on $\lambda_0$. For better visibility the values of $\xi$ are different for different lines. The horisontal axis corresponds to the canonically normalized field $\chi$, the vertical axis to the effective potential, all in Planck units.
• Figure 2: The dependence of the inflationary indexes $n_s$ and $r$ on $\xi$ and $\kappa$, the parameter $\lambda_0$ is fixed by the COBE normalisation. Along the nearly horisontal lines $\xi$ is fixed and $\kappa$ is varying within the interval $\{0.9,1.1\}$. We also show 1 and 2 $\sigma$ contours coming from the results of Planck Ade:2013uln.
• Figure 3: The same as in Fig. \ref{['fig:xigrid']}, but with the grid of constant $\kappa$ lines. The parameter $\xi$ is varying within the interval $\{5,30\}$.
• Figure 4: The same as in Fig. \ref{['fig:xigrid']}, but now on the plane $(n_s, dn_s/d\ln k)$, which includes the running of the scalar spectral index.
• Figure 5: The form of the effective potential which leads to $r=0.1$, $n_s=0.96$. The field values corresponding to the $N=57$ and $N=60$ e-foldings are marked by vertical lines, roughly indicating the observable window for inflation.