Volume 556, August 2013
|Number of page(s)||2|
|Section||Cosmology (including clusters of galaxies)|
|Published online||17 July 2013|
A curious relation between the flat cosmological model and the elliptic integral of the first kind
1 Charles University in Prague, Faculty of Mathematics and Physics, Astronomical Institute, V Holešovičkách 2, 18000 Prague 8, Czech Republic
2 Institute of Basic Science, Natural Sciences Campus, Sungkyunkwan University, Engineering Building 2, 2066 Seobu-ro, Jangan-gu, Suwon, 440-746 Gyeonggi-do, Korea
Received: 14 June 2013
Accepted: 16 June 2013
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.
Key words: cosmology: theory
© ESO, 2013
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