Topological Higgs inflation: Origin of Standard Model criticality

The measured values of the Higgs and top masses and of the strong gauge coupling constant point to the near-criticality of the Standard Model, where two vacua at the electroweak and Planck scales are quasidegenerate. We argue that the criticality is required by the occurrence of an eternal topological inflation induced by the Higgs potential. The role of this inflation is to continuously create a sufficiently flat and homogeneous Universe, providing the necessary initial condition for the subsequent slow-roll inflation that generates the density perturbations of the right magnitude. While the condition for the topological Higgs inflation is only marginally satisfied in the Standard Model, it can be readily satisfied if one introduces the right-handed neutrinos and/or the nonminimal coupling to gravity; currently unknown quantum gravity corrections to the potential may also help. We also discuss the $B-L$ Higgs inflation as a possible origin of the observed density perturbations. Its necessary initial condition, the restored $B-L$ symmetry, can be naturally realized by the preceding topological Higgs inflation.

Figure 1

The scale ${\mu }_{\min }$ that gives the minimum of the effective coupling ${\lambda }_{\text{eff}}$, under the criticality condition ${\lambda }_{\min }≔{\lambda }_{\text{eff}}({\mu }_{\min })=0$, as a function of $M_H$. The band width corresponds to the $2\sigma$ deviation of ${\alpha }_s$, with $1\sigma$ being given by ${\alpha }_s=0.1185\pm 0.0006$ [37]. The dotted lines show the $2\sigma$ band for $M_H$, with $1\sigma$ being given by $M_H=125.9\pm 0.4\mathrm{GeV}$ [37].

Figure 2

Allowed region in the prescription I (left) and II (right) in $\xi$ vs ${\mu }_{\min }$ plane, where the dark (light) region satisfies $|\eta ({\phi }_{\text{I}})|<1$ (1.4) and $|\eta ({\phi }_{\text{II}})|<1$ (1.4), respectively. In prescription I (left), ${\mu }_{\min }<M_P/\sqrt{\xi }$ is also imposed.