| Issue |
A&A
Volume 556, August 2013
|
|
|---|---|---|
| Article Number | A13 | |
| Number of page(s) | 2 | |
| Section | Cosmology (including clusters of galaxies) | |
| DOI | https://doi.org/10.1051/0004-6361/201322088 | |
| Published online | 17 July 2013 | |
Research Note
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
e-mail: meszaros@cesnet.cz
2 Institute of Basic Science, Natural Sciences Campus, Sungkyunkwan University, Engineering Building 2, 2066 Seobu-ro, Jangan-gu, Suwon, 440-746 Gyeonggi-do, Korea
e-mail: ripa.jakub@gmail.com
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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