Galaxies without dark matter halos?

In article ,
Dag Oestvang wrote:
wrote:

I will try to clarify: Unless V to a good approximation appears
from a cleverly arranged field of 4-velocities in flat space-time
(this is exact in the Milne model), there is no natural way to
interpret V in this way if the effects on V of curved space-time
on parallel transport is not negligible.

That's true. But in the low-redshift limit, the effects on V of
curved spacetime on parallel transport *are* negligible.

Proof: Try it and see! Neglect spacetime curvature and
parallel-transport V. In the low-redshift limit, you get the right
answer. Therefore, neglecting spacetime curvature didn't
do any harm. Spacetime curvature was negligible.


In other words; insofar as the effects on V coming from the
curvature of space-time can be neglected it is perfectly all
right to interpret V as coming from a field of 4-velocities in
flat space-time. But it is not if the size of V depends crucially
on space-time curvature.

I agree. But again, the last "if" clause is false in the limit
I'm considering.

Do you think that "the size of V depends crucially on space-time
curvature" in an Omega = 0 FRW Universe? (I certainly hope not,
since there is no curvature in this spacetime.) How about
in an Omega = 10^(-50) FRW Universe?

It seems that we mostly agree. This is my position: If the effects
of curved space-time on V are negligible then interpretations of
spectral shifts as Doppler effects in flat space-time are OK;
otherwise not. Do you agree?

Yes. But again, the "If" clause is false in the low-redshift
limit of an FRW Universe.

-Ted

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