Rapid numerical solutions for the Mukhanov-Sasaki equation

TL;DR

This paper introduces a fast numerical method for computing primordial power spectra by combining analytic approximations and matrix multiplication, significantly speeding up calculations for various wavenumbers.

Contribution

The authors present a novel technique that accelerates the computation of the Mukhanov-Sasaki equation solutions using analytic approximations and matrix operations, outperforming traditional methods.

Findings

Method achieves orders of magnitude speedup at intermediate and large wavenumbers.

Successfully applied to a stepped quadratic potential with kinetic dominance.

Demonstrates high accuracy and efficiency in challenging scenarios.

Abstract

We develop a novel technique for numerically computing the primordial power spectra of comoving curvature perturbations. By finding suitable analytic approximations for different regions of the mode equations and stitching them together, we reduce the solution of a differential equation to repeated matrix multiplication. This results in a wavenumber-dependent increase in speed which is orders of magnitude faster than traditional approaches at intermediate and large wavenumbers. We demonstrate the method's efficacy on the challenging case of a stepped quadratic potential with kinetic dominance initial conditions.