Inflection-point Higgs Inflation

Understand

Inflection-point inflation is an interesting possibility to realize a successful slow-roll inflation when inflation is driven by a single scalar field with its initial value below the Planck mass ($\phi_I \lesssim M_{Pl}$).

• In order for a renormalization group (RG) improved effective $\lambda \phi^4$ potential to develop an inflection-point, the quartic coupling $\lambda(\phi)$ must exhibit a minimum with an almost vanishing value in its RG evolution, namely $\lambda(\phi_I) \simeq 0$ and $\beta_{\lambda}(\phi_I) \simeq 0$, where $\beta_{\lambda}$ is the beta-function of the quartic coupling.
• As an example, we consider the minimal gauged $B-L$ extended Standard Model at the TeV scale, where we identify the $B-L$ Higgs field as the inflaton field.
• For a successful inflection-point inflation, which is consistent with the current cosmological observations, the mass ratios among the $Z^{\prime}$ gauge boson, the right-handed neutrinos and the $B-L$ Higgs boson are fixed.