But it's the standard way the luminosity distance is defined. [...] Units with c = 1 are used in the formulas. [...] Space alone is flat (within measurement uncertainties), but space-time is curved, because space expands with time. [...] It's not the easiest way to treat objects moving with the Hubble flow... [...] Yes, there are two (1+z) factors, one because fewer photons are emitted per unit time because "time was slower back then" (I know, not a very clear way to put it) and one because each photon is redshifted. The luminosity distance is defined with one (1+z) factor so that when you divide by its square you get (1+z)^-2. [...] No, because we're talking about the total luminosity of the galaxy -- if its length is contracted and its luminosity density is increased by the same factor, nothing changes. [...] What do you mean? It's not like this is an open question in cosmology. The implications of the FLRW metric have been well known for decades.

It's all baked into z. z is defined based on frequency change but the frequency change must also be the amount it appears to be slowed down, since e.g. you could measure the number of peaks in a light wave coming from a galaxy as a measure of time. For the benefit of others: in making this post Thomas is I expect motivated by my responses to his post here: https://protokol2020.wordpress.com/2013/09/06/embarrassing-images/#comments In an edit to my last comment, Thomas wrote: [...] In reply about the blue shift galaxies: they will indeed appear to be sped up from our perspective. Something moving toward us is slowed down in our reference frame by time dilation, but also appears sped up because light takes less and less time to get here. As with redshift, both of these effects are baked into z, so the final (apparent) speedup is what you get from z.