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 wave-number-dependent increase in speed which is orders of magnitude faster than traditional approaches at intermediate and large wave numbers. We demonstrate the method's efficacy on the challenging case of a stepped quadratic potential with kinetic dominance. We further generalize to a novel class of frozen initial conditions which prove capable of emulating a quantized primordial power spectrum.
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