1306.4736 (A. Meszaros et al.)

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

A. Meszaros, J. Ripa

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. The purpose of this article is to present such a relation also for the non-zero cosmological constant, if the universe is spatially flat. A definite integral is used. The integration ends in the elliptic integral of the first kind. The result shows that no numerical integration is needed for the non-zero cosmological constant, if the universe is spatially flat.

View original: http://arxiv.org/abs/1306.4736