Natural Inflation with Exponentially Small Tensor-To-Scalar Ratio

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~ 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 αₛ 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.