Running from Features: Optimized Evaluation of Inflationary Power Spectra

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.

21 pages, 14 figures; minor changes, matches published version

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• Generalized Slow Roll in the Unified Effective Field Theory of Inflation
• Probing features in inflaton potential and reionization history with future CMB space observations
• Nonlinear Excitations in Inflationary Power Spectra
• Primordial Black Holes as Dark Matter through Higgs Criticality
• Constraints on features in the inflationary potential from future Euclid data
• Effective field theory of degenerate higher-order inflation
• Primordial power spectrum features in phenomenological descriptions of inflation
• Effect of damped oscillations in the inflationary potential
• Reconciling tensor and scalar observables in G-inflation
• Can power spectrum observations rule out slow-roll inflation?
• From Non-trivial Geometries to Power Spectra and Vice Versa
• The running of featureful primordial power spectra
• Inflation Story: slow-roll and beyond
• The Black Hole Window on Cosmic Inflation