Cosmological redshift and Doppler shift

I'd like to ask anyone who's been following the discussion about the
low-redshift limit of the cosmological redshift to answer the
following question.  I'm going to list a sequence of statements, all
of which I believe.  I'll order them from least to most controversial.
At what point, if any, do you part company with me?


1. An observer in flat (Minkowski) spacetime measures the redshift of
   light from a source and finds z = Delta lambda/lambda = 0.01.  She
   can use the special-relativistic Doppler shift formula to determine
   the source's speed relative to her (getting the answer v =
   0.01c).

2. An observer in an open FRW spacetime with zero density (Omega = 0)
   measures the redshift of light from a source and finds z = 0.01.
   She can use She can use the special-relativistic Doppler shift
   formula to determine the source's speed relative to her.

3. An observer in an open FRW spacetime with density parameter Omega =
   10^(-50) measures the redshift of light from a source and finds z =
   0.01.  She uses the special-relativistic Doppler shift formula to
   calculate a speed.  To an excellent approximation, she can
   approximate spacetime as flat and interpret that number as the source's
   speed relative to her.

4. An observer in an open FRW spacetime with density parameter Omega =
   1 measures the redshift of light from a source and finds z = 0.01.
   She uses the special-relativistic Doppler shift formula to
   calculate a speed.  To a good approximation, she can approximate
   spacetime as flat and interpret that number as the source's speed
   relative to her.

(For statement 2, recall that the Omega = 0 FRW spacetime is exactly
the same as Minkowski spacetime.  For statement 3, note that over the
range of the observations, the geometry of spacetime differs from
Minkowski by less than one part in 10^50.)

-Ted

-- 
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