Inflection-point Higgs Inflation
  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. 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 $\alpha \simeq - 2.7
\times 10^{-3}\left(\frac{60}{N}\right)^2$ ($N$ is the $e$-folding number),
which can be tested in the near future.
