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Cosmological hydrogen recombination: The effect of extremely high-n states

Grin, Daniel and Hirata, Christopher M. (2010) Cosmological hydrogen recombination: The effect of extremely high-n states. Physical Review D, 81 (8). Art. No. 083005. ISSN 1550-7998.

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Calculations of cosmological hydrogen recombination are vital for the extraction of cosmological parameters from cosmic microwave background (CMB) observations, and for imposing constraints to inflation and reionization. The Planck mission and future experiments will make high precision measurements of CMB anisotropies at angular scales as small as ℓ∼2500, necessitating a calculation of recombination with fractional accuracy of ≈10^(-3). Recent work on recombination includes two-photon transitions from high excitation states and many radiative transfer effects. Modern recombination calculations separately follow angular momentum sublevels of the hydrogen atom to accurately treat nonequilibrium effects at late times (z<900). The inclusion of extremely high-n (n≳100) states of hydrogen is then computationally challenging, preventing until now a determination of the maximum n needed to predict CMB anisotropy spectra with sufficient accuracy for Planck. Here, results from a new multilevel-atom code (RecSparse) are presented. For the first time, “forbidden” quadrupole transitions of hydrogen are included, but shown to be negligible. RecSparse is designed to quickly calculate recombination histories including extremely high-n states in hydrogen. Histories for a sequence of values as high as n_(max)=250 are computed, keeping track of all angular momentum sublevels and energy shells of the hydrogen atom separately. Use of an insufficiently high n_(max) value (e.g., n_(max)=64) leads to errors (e.g., 1.8σ for Planck) in the predicted CMB power spectrum. Extrapolating errors, the resulting CMB anisotropy spectra are converged to ~0.5σ at Fisher-matrix level for n_(max)=128, in the purely radiative case.

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Hirata, Christopher M.0000-0002-2951-4932
Additional Information:© 2010 The American Physical Society. Received 12 November 2009; published 15 April 2010. The authors acknowledge useful conversations with Y. Ali-Haїmoud, N. Bode, A. Pullen, T. L. Smith, J. Chluba, J. A. Rubiño-Martín, and the participants of the July 2009 Paris Workshop on Cosmological Recombination. D. G. is supported by the Dan David Foundation and the Gordon and Betty Moore Foundation. C. H. is supported by DoE DE-FG03-92-ER40701, the National Science Foundation under Contract No. AST-0807337, and the Alfred P. Sloan Foundation.
Funding AgencyGrant Number
Dan David FoundationUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Department of EnergyDE-FG03-92-ER40701
Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:8
Classification Code:PACS: 98.70.Vc, 32.70.Cs, 32.80.Rm, 98.80.-k
Record Number:CaltechAUTHORS:20100527-132055279
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18481
Deposited By: Ruth Sustaita
Deposited On:27 May 2010 20:51
Last Modified:03 Oct 2019 01:43

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