A general and practical method for calculating cosmological distances

Abstract

The calculation of distances is of fundamental importance in extragalactic astronomy and cosmology. However, no practical implementation for the general case has previously been available. We derive a second-order differential equation for the angular size distance valid not only in all em homogeneous Friedmann-Lemaitre cosmological models, parametrised by ${\lambda }_0$ and ${\Omega }_0$, but also in inhomogeneous `on-average' Friedmann-Lemaitre models, where the inhomogeneity is given by the (in the general case redshift-dependent) parameter $\eta$. Since most other cosmological distances can be obtained trivially from the angular size distance, and since the differential equation can be efficiently solved numerically, this offers for the first time a practical method for calculating distances in a large class of cosmological models. We also briefly discuss our numerical implementation, which is publicly available.

12 pages + 12 FORTRAN source files + PostScript User's Guide. Identical versions of everything available from http://www.hs.uni-hamburg.de/english/persons/helbig/Research/Publications/Inf o/angsiz.html or ftp://ftp.uni-hamburg.de/pub/unihh/astro/angsiz.tar-gz . Paper version available on request. Accepted by A&A. Changes: typos corrected, primarily in Appendix B. No changes to FORTRAN code or User's Guide. All versions mentioned here are complete; the published version will have the appendices published electronically at CDS

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