140 Cosmological models
(1) theredshift, basically a time-dilation effect for all measurements of the
source (determined by the radial component of velocity);
(2) thearea distance, equivalent to the angular diameter distance in RW
geometries, and also equivalent (up to a redshift factor) to the luminosity
distance in all relativistic cosmological models, because of the reciprocity
theorem [26]—this can best be calculated from the geodesic deviation
equation [54]; and
(3) number counts, determined by (i) the number of objects in a given
volume, (ii) the relation of that volume to increments in distance measures
(determined by the spacetime geometry) and (iii) the selection and detection
effects that determine which sources we can actually identify and measure
(difficulties in detection being acute in the case of dark matter).Thus to determine the spacetime geometry in these models, we need to
correlate at least two of these variables against each other. Further observational
data which must be consistent with the other observations comes from the
following sources:
(4) background radiation spectra at all wavelengths particularly the 3K
blackbody relic radiation (‘CBR’); and
(5) the ‘relics’ of processes taking place in the hot big-bang era,for
example the primeval element abundances resulting from baryosynthesis and
nucleosynthesis in the hot early universe (and the CBR anisotropies and
present large-scale structures can also be regarded in this light, for they are
evidence about density fluctuations, which are one form of such relic).The observational relations in FL models are covered in depth in other
reports to this meeting (and see also [26, 33]), so I will just comment on two
aspects here.
Selection/detection effects:The way we detect objects from available images
depends on both their surface brightness and their apparent size. Thus
we essentially needtwo variablesto adequately characterize selection and
detection effects; it simply is not adequate to discuss such effects on the
basis of apparent magnitude or flux alone [47]. Hence one should regard with
caution any catalogues that claim to be magnitude limited, for that cannot be
an adequate criteria for detection limits; such catalogues may well be missing
out many low surface-brightness objects.
Minimum angles and trapping surfaces:For ordinary matter, there is a redshift
z(such that apparent sizes of objects of fixed linear size reach a minimum at
z=z(, and for larger redshift look larger again. What is happening here is
that the universe as a whole is acting as a giant gravitational lens, refocusing
our past light cone as a whole [26]; in an Einstein–de-Sitter universe, this
happens atz(= 5 /4; in a low density universe, it happens at aboutz=4.
This refocusing means that closed trapped surfaces occur in the universe, and