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
*homogeneous* Friedmann-Lemaître cosmological models, parametrised
by $\lambda_{0}$ and $\Omega_{0}$, but also in *inhomogeneous*
`on-average' Friedmann-Lemaître models, where the inhomogeneity is
given by
the (in the general case redshift-dependent) parameter $\eta$. Since most
other 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.

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last modified on Tuesday, December 31, 2013 at 11:06:37 PM by helbig@ascameltro.multivax.de (remove animal to reply)