From: Robert A. Knop Jr. (robert.a.knop@vanderbilt.edu)
Date: Tue Apr 15 2003 - 07:27:44 PDT
I got thinking about this, and I'm questioning whether using CMB
redshifts is the right thing to do in cosmology. In fact, I think the
heliocentric (or, really, geocentric) redshifts may be better; the right
thing to do is probably CMB redshfits with some corrections.
What got me thinking about this was that I had forgotten to correct
low-z SN redshifts to CMB before the cosmology fits I posted yesterday.
When I went and put that in, the chisquares all got worse, due to the
individual residuals for some low-z supernovae getting worse.
As I thought about it, I was thinking about the derivations of how
luminosity distance relates to angular diameter distance. There is a
term of (1+z) that gets put in there due to time dilation. Now, that
time dilation will happen whether the z is from a cosmological redshift
or a doppler shift due to our motion relative to the CMB. As such,
we're failing to account for some fraction of the time dilation when we
use CMB redshifts rather than redshifts as observed by us.
I will have to think harder about the rest of the derivation; it seems
implausible to me that the luminosity distance equation will give the
"right" magnitude decrement at a given z if that z is not entirely from
a cosmological redshift, but I may be confused on this. In any event, I
*am* convinced becuase of what's in the previous paragraph that just
blindly using CMB redshifts *will* give you slightly the wrong magnitude
decrement.
The question remains: do we have to do something more sophisticated, or
will blindly using helocentric redshifts do the right thing?
Has anybody thought about this in greater detail? (I will go back and
pore over this, because I've thought close to this in greater detail in
the past, and made notes when I was doing it.)
-Rob
-- --Prof. Robert Knop Department of Physics & Astronomy, Vanderbilt University robert.a.knop@vanderbilt.edu
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