Inflection-Point Inflation in a Hyper-Charge Oriented U(1)ₓ Model

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 value during inflation below the Planck mass (ϕ⌄I ≲ M⌄P1). In order for a renormalization group (RG) improved effective λϕ⁴ potential to develop an inflection point, the running quartic coupling λ(ϕ) must exhibit a minimum with an almost vanishing value in its RG evolution, namely λ(ϕ⌄I) ≃ 0 and β⌄λ (ϕ⌄I) ≃ 0, where β⌄λ is the beta function of the quartic coupling. In this paper, we consider the inflection-point inflation in the context of the minimal U(1)ₓ extended Standard Model (SM), a generalization of the minimal U(1)⌄(B-L) model, where the U(1)ₓ symmetry is realized as a linear combination of the SM U(1)ᵧ and the U(1)⌄(B-L) gauge symmetries. We identify the U(1)ₓ Higgs field with the inflaton field. For successful inflection-point inflation to be consistent with the current cosmological observations, the mass ratios among the U(1)ₓ gauge boson, the right-handed neutrinos, and the U(1)ₓ Higgs boson are fixed. Focusing on the case that the U(1)ₓ gauge symmetry is mostly oriented towards the SM U(1)ᵧ direction, we investigate a consistency between the inflationary predictions and the latest LHC Run 2 results on the search for a narrow resonance with the dilepton final state. In addition, the inflection-point inflation provides a unique prediction for the running of the spectral index α ≃ −2.7 × 10⁻³(60/N)² (N is the e-folding number), which can be tested in the near future.

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Keywords
Extensions of gauge sector, Inflation, Particles & Fields
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