A curious relation between the flat cosmological model and the elliptic integral of the first kind

Context. The dependence of the luminosity distance on the redshift has a key importance in the cosmology. This dependence can well be given by standard functions for the zero cosmological constant. Aims. The purpose of this article is to present a similar relation also for the non-zero cosmological...

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Bibliographic Details
Published inAstronomy and astrophysics (Berlin) Vol. 556; pp. 1 - 2
Main Authors Meszaros, A, Ripa, J
Format Journal Article
LanguageEnglish
Published EDP Sciences 01.08.2013
Subjects
Astronomy
Cosmological constant
Cosmology
cosmology: theory
Elliptic integrals
Flats
Mathematical analysis
Universe
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Summary:Context. The dependence of the luminosity distance on the redshift has a key importance in the cosmology. This dependence can well be given by standard functions for the zero cosmological constant. Aims. The purpose of this article is to present a similar relation also for the non-zero cosmological constant, if the universe is spatially flat. Methods. A definite integral was used. Results. The integration ends in the elliptic integral of the first kind. Conclusions. The result shows that no numerical integration is needed for the non-zero cosmological constant if the universe is spatially flat.
Bibliography:istex:DFEAD2506097D23FC747AD5D1E4CAAF8FE79F281
ark:/67375/80W-3BZMZGXZ-K
e-mail: meszaros@cesnet.cz
bibcode:2013A%26A...556A..13M
dkey:10.1051/0004-6361/201322088
publisher-ID:aa22088-13
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0004-6361
1432-0746
DOI:10.1051/0004-6361/201322088