SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 338, 777-780 (1998)

Previous Section Next Section Title Page Table of Contents

2. Distance and volume measures in general FLRW cosmologies

We assume a homogeneous and isotropic universe described by a Robertson-Walker metric (Weinberg 1972):

[EQUATION]

or in the form

[EQUATION]

where

[EQUATION]

The relation of the measurables to the unmeasurables is (Lightman et al. 1975; Carroll, Press & Turner 1992)

[EQUATION]

[EQUATION]

where [FORMULA] is the present time of the universe, and [FORMULA], [FORMULA] and [FORMULA] are the angular diameter distance, the proper motion distance and the luminosity distance respectively. Distances used in lensing theory are the angular diameter distances (Schneider, Ehlers & Falco 1992). From Eqs. 3and 4, one can derive an important relation

[EQUATION]

where [FORMULA] and [FORMULA] are the angular distances from the lens to the source and from the observer to the source, respectively.

Using the Einstein field equation, it can be shown that the relation of the comoving distance [FORMULA] to the redshift for the general FLRW cosmologies is (see Eq. 6)

[EQUATION]

For our end, the comoving volume dV is more convenient than the traditional physical volume. Within the shell [FORMULA] at [FORMULA], dV reads (Gott, Park & Lee 1989)

[EQUATION]

[EQUATION]

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1998

Online publication: September 17, 1998
helpdesk.link@springer.de