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