Inflection-point Higgs Inflation

Abstract

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 ($\ddot{I}{•}_I\lesssim M_{Pl}$). In order for a renormalization group (RG) improved effective $\hat{I}»\ddot{I}{•}^4$ potential to develop an inflection-point, the quartic coupling $\hat{I}»(\ddot{I}•)$ must exhibit a minimum with an almost vanishing value in its RG evolution, namely $\hat{I}»(\ddot{I}{•}_I)\simeq 0$ and ${\hat{I}}_{\hat{I}}^2»(\ddot{I}{•}_I)\simeq 0$, where ${\hat{I}}_{\hat{I}}^2»$ 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 $\hat{I}\pm \simeq -2.7\times 10^{-3}{\left(\frac{60}{N}\right)}^2$ ($N$ is the $e$-folding number), which can be tested in the near future.

16 pages, 3 figures, analysis for the end of inflation revised, typos corrected. Accepted for publication in PRD