Natural Inflation with Exponentially Small Tensor-To-Scalar Ratio

TL;DR

This paper shows that natural (axion) inflation can fit Planck 2018 data while predicting an extremely small tensor-to-scalar ratio, undetectable by current experiments but testable via spectral index running.

Contribution

It introduces a natural inflation model with an exponentially suppressed tensor-to-scalar ratio driven by the radial component dynamics, aligning with observational constraints.

Findings

Tensor-to-scalar ratio r ~ 10^{-15} predicted

Model consistent with Planck 2018 measurements

Running of spectral index within reach of future experiments

Abstract

We demonstrate that "natural inflation", also known as "axion inflation", can be compatible with Planck 2018 measurements of the cosmic microwave background, while predicting an exponentially small tensor-to-scalar ratio, e.g., $r\sim 10^{-15}$. The strong suppression of $r$ arises from dynamics of the radial component of the complex scalar field, whose phase is the axion. Such tiny values of $r$ remain well below the threshold for detection by CMB-S4 or Simons Observatory B-mode searches. The model is testable with the running $\alpha_s$ of the spectral index, which is within reach of next-generation CMB and large-scale structure experiments, motivating the running as a primary science goal for future experiments.