Computing the Primordial Power Spectra Directly

TL;DR

This paper introduces differential equations and asymptotic expansions to compute primordial power spectra efficiently, bypassing complex oscillatory mode simulations during inflation.

Contribution

It provides a novel method to directly calculate power spectra without numerically simulating oscillating mode functions.

Findings

Derivation of simple differential equations for power spectra

Asymptotic expansions valid until a few e-foldings before horizon crossing

Reduction of computational complexity in inflationary spectra calculations

Abstract

The tree order power spectra of primordial inflation depend upon the norm-squared of mode functions which oscillate for early times and then freeze in to constant values. We derive simple differential equations for the power spectra, that avoid the need to numerically simulate the physically irrelevant phases of the mode functions. We also derive asymptotic expansions which should be valid until a few e-foldings before first horizon crossing, thereby avoiding the need to evolve mode functions from the ultraviolet over long periods of inflation.