Astronomy and Astrophysics – Astrophysics – Cosmology and Extragalactic Astrophysics
Scientific paper
2010-12-02
Phys.Rev.D83:103521,2011
Astronomy and Astrophysics
Astrophysics
Cosmology and Extragalactic Astrophysics
10 pages, 6 figures. Published version. Codes available at http://www.phas.ubc.ca/~francis
Scientific paper
10.1103/PhysRevD.83.103521
Prior to recombination photons, electrons, and atomic nuclei rapidly scattered and behaved, almost, like a single tightly-coupled photon-baryon plasma. We investigate here the accuracy of the tight-coupling approximation commonly used to numerically evolve the baryon and photon perturbation equations at early times. By solving the exact perturbations equations with a stiff solver starting deep in the radiation-dominated epoch we find the level of inaccuracy introduced by resorting to the standard first-order tight-coupling approximation. We develop a new second-order approximation in the inverse Thomson opacity expansion and show that it closely tracks the full solution, at essentially no extra numerical cost. We find the bias on estimates of cosmological parameters introduced by the first-order approximation is, for most parameters, negligible. Finally, we show that our second-order approximation can be used to reduce the time needed to compute cosmic microwave background angular spectra by as much as ~17%.
Cyr-Racine Francis-Yan
Sigurdson Kris
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