Advanced search
1 file | 354.63 KB Add to list

Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology

Maarten Baes (UGent) , Peter Camps (UGent) and Dries Van De Putte (UGent)
Author
Organization
Abstract
Accurate and efficient methods to evaluate cosmological distances are an important tool in modern precision cosmology. In a flat Lambda cold dark matter (CDM) cosmology, the luminosity distance can be expressed in terms of elliptic integrals. We derive an alternative and simple expression for the luminosity distance in a flat Lambda CDM based on hypergeometric functions. Using a timing experiment, we compare the computation time for the numerical evaluation of the various exact formulae, as well as for two approximate fitting formulae available in the literature. We find that our novel expression is the most efficient exact expression in the redshift range of z greater than or similar to 1. Ideally, it can be combined with the expression based on Carlson's elliptic integrals in the range of z less than or similar to 1 for high-precision cosmology distance calculations over the entire redshift range. On the other hand, for practical work where relative errors of about 0.1 per cent are acceptable, the analytical approximation proposed by Adachi & Kasai (2012) is a suitable alternative.
Keywords
methods: analytical, methods: numerical, cosmology: theory, distance scale, GAUSS HYPERGEOMETRIC FUNCTION, KIND RESEARCH-NOTE, ELLIPTIC INTEGRALS, 1ST KIND, CONSTANT

Downloads

  • Baes et al. 2017.pdf
    • full text
    • |
    • open access
    • |
    • PDF
    • |
    • 354.63 KB

Citation

Please use this url to cite or link to this publication:

MLA
Baes, Maarten, Peter Camps, and Dries Van De Putte. “Analytical Expressions and Numerical Evaluation of the Luminosity Distance in a Flat Cosmology.” MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 468.1 (2017): 927–930. Print.
APA
Baes, M., Camps, P., & Van De Putte, D. (2017). Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, 468(1), 927–930.
Chicago author-date
Baes, Maarten, Peter Camps, and Dries Van De Putte. 2017. “Analytical Expressions and Numerical Evaluation of the Luminosity Distance in a Flat Cosmology.” Monthly Notices of the Royal Astronomical Society 468 (1): 927–930.
Chicago author-date (all authors)
Baes, Maarten, Peter Camps, and Dries Van De Putte. 2017. “Analytical Expressions and Numerical Evaluation of the Luminosity Distance in a Flat Cosmology.” Monthly Notices of the Royal Astronomical Society 468 (1): 927–930.
Vancouver
1.
Baes M, Camps P, Van De Putte D. Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY. 2017;468(1):927–30.
IEEE
[1]
M. Baes, P. Camps, and D. Van De Putte, “Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology,” MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, vol. 468, no. 1, pp. 927–930, 2017.
@article{8516574,
  abstract     = {Accurate and efficient methods to evaluate cosmological distances are an important tool in modern precision cosmology. In a flat Lambda cold dark matter (CDM) cosmology, the luminosity distance can be expressed in terms of elliptic integrals. We derive an alternative and simple expression for the luminosity distance in a flat Lambda CDM based on hypergeometric functions. Using a timing experiment, we compare the computation time for the numerical evaluation of the various exact formulae, as well as for two approximate fitting formulae available in the literature. We find that our novel expression is the most efficient exact expression in the redshift range of z greater than or similar to 1. Ideally, it can be combined with the expression based on Carlson's elliptic integrals in the range of z less than or similar to 1 for high-precision cosmology distance calculations over the entire redshift range. On the other hand, for practical work where relative errors of about 0.1 per cent are acceptable, the analytical approximation proposed by Adachi & Kasai (2012) is a suitable alternative.},
  author       = {Baes, Maarten and Camps, Peter and Van De Putte, Dries},
  issn         = {0035-8711},
  journal      = {MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY},
  keywords     = {methods: analytical,methods: numerical,cosmology: theory,distance scale,GAUSS HYPERGEOMETRIC FUNCTION,KIND RESEARCH-NOTE,ELLIPTIC INTEGRALS,1ST KIND,CONSTANT},
  language     = {eng},
  number       = {1},
  pages        = {927--930},
  title        = {Analytical expressions and numerical evaluation of the luminosity distance in a flat cosmology},
  url          = {http://dx.doi.org/10.1093/mnras/stx537},
  volume       = {468},
  year         = {2017},
}

Altmetric
View in Altmetric
Web of Science
Times cited: