From: Eric Linder (evlinder@lbl.gov)
Date: Wed Apr 16 2003 - 09:34:58 PDT
It looks like I've been brought into the middle of this, so I'm not sure
of the exact context, but it sounds to me like Rob's analysis is
correct.
In r_l(z), the quantity z is just a useful parametrization of cosmic
distance or time; one could equally write r_l(a) or r_l(t) or
r_l(r_coordinate). So the z here should be the redshift due solely to
the global expansion.
For the factors 1+z, these comes from photon frequency shift and time
dilation, i.e. the 0 and 1 components of the photon four-momentum.
Therefore all influences on these must be taken into account equally.
This is properly multiplicative in 1+z, not additive in z, since the
ratio of frequencies (or wavelengths or momenta) goes as 1+z. That is,
(1+z)_total = (1+z)_cosmic * (1+z)_peculiarvelocity
Of course when one z is small, it looks like adding z's.
Cheers,
Eric
p.s. Five more messages on this subject came into my inbox while I was
writing this! I'll respond further once I've read them.
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