A more accurate analytic calculation of the spectrum of cosmological perturbations produced during inflation

TL;DR

This work presents analytic expressions for the spectra of scalar curvature perturbations and gravitational waves generated during inflation, including exact results for power-law inflation, small-angle natural inflation, and general slow-roll scenarios. By deriving the Mukhanov–Sasaki formalism with constant slow-roll parameters and extending to second order, the authors quantify corrections to the standard first-order spectra and spectral tilts. The results sharpen the connection between inflationary dynamics and observable perturbation spectra, and demonstrate that certain models can yield sizable deviations from naive estimates if precision measurements of the spectral indices improve. Overall, the paper provides a unified framework to compute accurate perturbation spectra across key inflationary regimes and underscores the impact of higher-order corrections on interpreting observations.

Abstract

Formulae are derived for the spectra of scalar curvature perturbations and gravitational waves produced during inflation, special cases of which include power law inflation, natural inflation in the small angle approximation and inflation in the slow roll approximation.