Also parameters like flux density, angular size, distances and volumes are in
cosmological models different than in every day life (see Condon, 1988).
Consider an isotropic source at redshift with spectral luminosity
at
frequency
(measured in the source frame). Its spectral flux density
measured at the same frequency
(in the observers frame) will be
where is the area of the sphere centered on the source and containing the
observer and
is the spectral index between
and
in the observer's frame. The
term expresses the special relativistic Doppler correction. The geometric and
expansion dynamics of the universe only appear in
. Longair (1978) defined the
"effective distance" as
. The area of the sphere
centered on the observer and containing a source at redshift
is always
. Hence, the relation between (projected) lineair size
and measured angular size
is
The "bolometric luminosity distance" is defined by
In Friedmann models (cosmological constant ) with zero pressure,
density parameter
, and current Hubble parameter
, the
effective distance is given (Mattig, 1958) as
This formula is numerical unstable for small and therefore the
transformation
is better for numerical calculations. For particular values of ,
reduces to the simpler forms
Finally the rotation measure changes rapidly with increasing redshift. If the
rotation measure in the observers frame is then the rotation measure
in the source frame will be