Signatures of Planck Corrections in a Spiralling Axion Inflation Model

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 $\Phi$. 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 $\phi^{4/3}$ chaotic inflation model. Planck corrections become important when the dimensionless coupling $\xi$ of $|\Phi|^{2}$ to the topological charge density of the strongly-coupled gauge sector $F \tilde{F}$ satisfies $\xi \sim 1$. For values of $|\Phi|$ which allow the Planck corrections to be understood via an expansion in powers of $|\Phi|^{2}/M_{Pl}^{2}$, we show that their effect is to produce a significant modification of the tensor-to-scalar ratio from its $\phi^{4/3}$ chaotic inflation value without strongly modifying the spectral index. In addition, to leading order in $|\Phi|^2/M_{Pl}^{2}$, the Planck modifications of $n_{s}$ and $r$ satisfy a consistency relation, $\Delta n_{s} = - \Delta r/16$. Observation of these modifications and their correlation would allow the model to be distinguished from a simple $\phi^{4/3}$ chaotic inflation model and would also provide a signature for the influence of leading-order Planck corrections.