Running from Features: Optimized Evaluation of Inflationary Power Spectra

TL;DR

This paper introduces an optimized generalized slow-roll method for accurately evaluating inflationary power spectra with features, improving predictions especially when features occur over small efolds, surpassing standard approaches.

Contribution

It develops a new optimized next-order generalized slow-roll approach that accurately predicts power spectra with features over small efolds, outperforming traditional methods.

Findings

Optimized approach predicts observables to 10^{-3} accuracy.

Standard second-order methods are less accurate than leading-order.

Explicit relations between potential parameters and spectral features in monodromy models.

Abstract

In models like axion monodromy, temporal features during inflation which are not associated with its ending can produce scalar, and to a lesser extent, tensor power spectra where deviations from scale-free power law spectra can be as large as the deviations from scale invariance itself. Here the standard slow-roll approach breaks down since its parameters evolve on an efolding scale $\Delta N$ much smaller than the efolds to the end of inflation. Using the generalized slow-roll approach, we show that the expansion of observables in a hierarchy of potential or Hubble evolution parameters comes from a Taylor expansion of the features around an evaluation point that can be optimized. Optimization of the leading-order expression provides a sufficiently accurate approximation for current data as long as the power spectrum can be described over the well-observed few efolds by the local tilt and running. Standard second-order approaches, often used in the literature, ironically are worse than leading-order approaches due to inconsistent evaluation of observables. We develop a new optimized next-order approach which predicts observables to $10^{-3}$ even for $\Delta N\sim 1$ where all parameters in the infinite hierarchy are of comparable magnitude. For models with $\Delta N \ll 1$, the generalized slow-roll approach provides integral expressions that are accurate to second order in the deviation from scale invariance. Their evaluation in the monodromy model provides highly accurate explicit relations between the running oscillation amplitude, frequency and phase in the curvature spectrum and parameters of the potential.