> The reason to use the speeds and not the distances in the papers is that we actually measure the speeds (redshifts, to be precise)
Comoving coordinates are a more important consideration. The coordinate distance (which is the comoving distance) between galaxies is fixed in the standard cosmological model.
Standard candles like supernova light curves do indeed rely on redshift, and it is straightforward to convert cosmological redshift into a recession velocity.
However, standard rulers include angle-diameter-surface brightness relations which do not measure redshift; one calculates the redshift for these objects through e.g. the Mattig or Sigma-D relation.
Extragalactic distance ladders combine these and other classes of observables.
Using redshift and a scale factor for cosmological distances rather than Gly or Gpc also defocuses one from distracting differences between cosmological proper distance and relativistic proper length, for example, while bringing into focus peculiar velocity. It's also handy when dealing with different systems of units, such as geometrized ones in which G=c=1, as is common practice in cosmology.
Just by way of example, starting with your H_0 value, and being slightly sloppy (especially wrt sigfigs), for ~1 Gly, I plug in H_0 = 70, z = 0.076 , \Omega_{m} = 0.31, and the standard values for the other densities, and get four useful distances: comoving = 750 h^-1 / Mly, proper distance at z=0 = 1043 Mly, proper distance at z=0.078(a=0.928) = 969.4 Mly, time interval = 1.004 Gy.
Is it really useful (rather than simply nifty) to think of a galaxy at a slightly greater redshift moving away at ~ 2x Earth's diameter every second?
Thanks. You, of course, have much deeper knowledge of the subject, I hoped somebody with more knowledge will eventually comment and add some more details.
For those who want to know what you talk about (at the start) and I've avoided for simplicity, lacking some more exact link, I hope wikipedia is good enough:
If I may ask, not doing astrophysics professionally, but being interested, I don't understand why you started with z = 0.076 and then calculated proper distance at z=0.078. I also don't know what (a=0.928) there stands for.
The two proper distances can be thought of as, for the larger, what a notional instantaneous (>> FTL) analogue of radar measurement would decide the distance to the galaxy we are observing is, and for the smaller, what we would read if we had optical telescopes that could read the display of such a measurement device showing a counterpart in the distant galaxy what the instantaneous distance to us is.
(Or instead of an instant FTL analogue of radar, you could use a pair extremely long measuring tapes with the 0 end anchored on the observed party; if we look at a telescope at their tape's indicator, it would read 969.4 Mly, but looking at our own tape would read 1043 Mly.)
The numbers are close because ~1 Gly is near enough that the metric expansion of space hasn't carried our galaxy cluster and theirs very far apart in the past billion years.
They would see similar numbers looking at a galaxy at z=0.076 in a different part of their sky than where the Milky Way is; we would see a different and almost certainly higher redshift when looking at that galaxy from here.
Comoving coordinates are a more important consideration. The coordinate distance (which is the comoving distance) between galaxies is fixed in the standard cosmological model.
Standard candles like supernova light curves do indeed rely on redshift, and it is straightforward to convert cosmological redshift into a recession velocity.
However, standard rulers include angle-diameter-surface brightness relations which do not measure redshift; one calculates the redshift for these objects through e.g. the Mattig or Sigma-D relation.
Extragalactic distance ladders combine these and other classes of observables.
Using redshift and a scale factor for cosmological distances rather than Gly or Gpc also defocuses one from distracting differences between cosmological proper distance and relativistic proper length, for example, while bringing into focus peculiar velocity. It's also handy when dealing with different systems of units, such as geometrized ones in which G=c=1, as is common practice in cosmology.
Just by way of example, starting with your H_0 value, and being slightly sloppy (especially wrt sigfigs), for ~1 Gly, I plug in H_0 = 70, z = 0.076 , \Omega_{m} = 0.31, and the standard values for the other densities, and get four useful distances: comoving = 750 h^-1 / Mly, proper distance at z=0 = 1043 Mly, proper distance at z=0.078(a=0.928) = 969.4 Mly, time interval = 1.004 Gy.
Is it really useful (rather than simply nifty) to think of a galaxy at a slightly greater redshift moving away at ~ 2x Earth's diameter every second?