Volume 573, January 2015
|Number of page(s)||2|
|Section||Cosmology (including clusters of galaxies)|
|Published online||17 December 2014|
On the relation between the non-flat cosmological models and the elliptic integral of first kind
Charles University in Prague, Faculty of Mathematics and Physics,
Astronomical Institute, V
Holešovičkách 2, 180
00 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: 22 October 2014
Accepted: 25 October 2014
Context. Recently we have found an analytic integration formula that describes the dependence of the luminosity distance on the redshift for the flat cosmological model with a non-zero cosmological constant.
Aims. The purpose of this article is to search for a similar relation for the non-flat models.
Methods. A Taylor series was used.
Results. The elliptic integral of the first kind can indeed be applied.
Conclusions. The result shows that a combination of the numerical integration with the previous analytic formula can also be useful for the nearly flat cosmological models.
Key words: cosmology: theory
© ESO, 2014
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