Rapid numerical solutions for the Mukhanov-Sasaki equation

Understand

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.