Abstract
The minimal sub-Planckian axion inflation model accounts for a large scalar-to-tensor ratio via a spiralling trajectory in the field space of a complex field Φ. Here we consider how the predictions of the model are modified by Planck scale-suppressed corrections. In the absence of Planck corrections the model is equivalent to a ϕ4/3 chaotic inflation model. Planck corrections become important when the dimensionless coupling ξ of |Φ|2 to the topological charge density of the strongly-coupled gauge sector F F̃ satisfies ξ ∼ 1. For values of |Φ| which allow the Planck corrections to be understood via an expansion in powers of |Φ|2/MPl2, we show that their effect is to produce a significant modification of the tensor-to-scalar ratio from its ϕ4/3 chaotic inflation value without strongly modifying the spectral index. In addition, to leading order in |Φ|2/MPl2, the Planck modifications of ns and r satisfy a consistency relation, Δ ns = −Δr/16. Observation of these modifications and their correlation would allow the model to be distinguished from a simple ϕ4/3 chaotic inflation model and would also provide a signature for the influence of leading-order Planck corrections.
Highlights
The minimal sub-Planckian axion inflation model accounts for a large scalar-totensor ratio via a spiralling trajectory in the field space of a complex field Φ
For values of |Φ| which allow the Planck corrections to be understood via an expansion in powers of |Φ|2/MP2l, we show that their effect is to produce a significant modification of the tensor-to-scalar ratio from its φ4/3 chaotic inflation value without strongly modifying the spectral index
We have considered the effect of leading-order Planck corrections on the minimal subPlanckian axion inflation model
Summary
The minimal sub-Planckian axion inflation model [11] is structurally similar to the KSVZ axion model [16, 17]. For a range of values of Λsc and ξ, this potential has a spiralling groove inscribed on the |Φ|4 potential in the complex plane3 [11] Inflation occurs along this groove (very close to the angular or axion direction), allowing a super-Planckian change in the inflaton field while. One must assume that the additive Planck corrections are suppressed by at least a factor of λ, which is a much smaller suppression than would be required if the field were super-Planckian during inflation This suppression is not implausible if the renormalizable and non-renormalizable potential terms have a common origin in the complete theory, or if λ represents a symmetry-breaking effect such that the complete potential is exactly zero in the limit λ → 0. The sub-Planckian value of |Φ| predicted by the model allows such corrections to be controlled and their effects to be understood via an expansion in |Φ|2/MP2l
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