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 (${\varphi }_I\lesssim M_{\mathrm{Pl}}$). In order for a renormalization group (RG) improved effective $\lambda {\varphi }^4$ potential to develop an inflection point, the quartic coupling $\lambda (\varphi )$ must exhibit a minimum with an almost vanishing value in its RG evolution, namely $\lambda ({\varphi }_I)\simeq 0$ and ${\beta }_{\lambda }({\varphi }_I)\simeq 0$, 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. Our scenario can be tested in the future collider experiments such as the high-luminosity LHC and the SHiP experiments. In addition, the inflection-point inflation provides a unique prediction for the running of the spectral index $\alpha \simeq -2.7\times {10}^{-3}{(\frac{60}{N})}^2$ ($N$ is the $e$-folding number), which can be tested in the near future.

• Received 4 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.035035