Institute of Astronomy

oscode: fast solutions of oscillatory ODEs in cosmology

SpeakerTalk DateTalk Series
Fruzsina Agocs29 January 2020Institute of Astronomy Seminars

Abstract

Bayesian analysis of the cosmic microwave background (CMB) allows us to constrain cosmological parameters and infer the physics of the early
universe. The forward modelling phase of Bayesian inference involves calculation of the likelihood function of the model parameters, which requires one to numerically solve linear, ordinary differential equations with oscillatory solutions efficiently. I'll present a novel numerical routine, oscode, with associated open-source software, for such purposes. The method makes use of the Wentzel--Kramers--Brillouin approximation used in quantum mechanics to rapidly traverse highly oscillatory regions of the solution, giving a significant speedup compared to Runge--Kutta-like methods. Its efficiency is demonstrated on physical examples of the Schrödinger equation and the Mukhanov--Sasaki
equation; the latter is solved to generate primordial power spectra of
curvature perturbations in different cosmological scenarios.

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