For a given black body radiation curve, would the changes to the spectrum resulting from cosmological expansion and those from Doppler effects be distinguishable on the basis of the shapes of the resulting curves alone? Or, put another way, starting from the same spectrum, can both processes produce the same observation (for suitably chosen magnitudes of expansion or velocity)?
Answer
The redshift due to cosmological expansion is identical to a Doppler shift in its effect on the spectrum of any source. To be specific, both phenomena "stretch" all wavelengths by the same factor.
There's a very good reason for this: in a suitable coordinate system, the cosmological redshift is a Doppler shift.
You'll find statements in some textbooks saying that this isn't true, but a weak version of this statement, which is nonetheless strong enough to explain why the effects on the spectra are identical, is uncontroversially true. To be specific, the redshift of a distant galaxy can be thought of as the accumulation of many infinitesimal Doppler shifts along the line of sight. (Each member of a family of comoving observers is in motion relative to her neighbor, and each can "watch" the redshift build up gradually due to these relative velocities.)
One perspective on this subject (mine, to be precise) can be found in this paper. Even if you don't like our point of view in this paper, our description of and references to other treatments may be of interest.
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