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Taking Hubble's law into account, what is the velocity of the most distant galaxies relative to Earth? Yes, I know that it is actually space that is expanding, (so, it is not their real velocity), but at what speed relative to Earth are they receding from us?

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    $\begingroup$ Roughly $3.3c$. $\endgroup$ – pela Jun 9 '17 at 10:52
  • $\begingroup$ No it's not, it's 2.3c. @pela $\endgroup$ – Rob Jeffries Jun 18 '17 at 23:08
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    $\begingroup$ @RobJeffries: Yes, if you interpret the question as the most distant known galaxy. I interpreted it as the most distant galaxy in the observable Universe (assuming the cosmological principle holds true, so that there are galaxies out there, even though we won't see them because the lookback time is so large that it looks to us as though they haven't formed yet). $\endgroup$ – pela Jun 19 '17 at 8:12
  • $\begingroup$ @pela We cannot say anything about the recession velocities of things that are causally outside the observable universe. In the observable universe we know (or think) that galaxies cannot have formed prior to redshift 20. This gives an upper limit to the recession velocity of 2.5c. $\endgroup$ – Rob Jeffries Jun 19 '17 at 11:13
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    $\begingroup$ @RobJeffries: I understand what you mean. It's merely a question of how the OP is interpreted. What I mean is that, if the cosmological principle holds true, then there are galaxies all the way out to the "edge" of the observable Universe (and probably beyond, but I don't consider those). These galaxies exist right now, they are at the same evolutionary state as the Local Universe, and they recede at v = 3.3c. You are of course right that, because of the finite speed of light, we look so far back in time that, to us, they haven't formed yet. $\endgroup$ – pela Jun 19 '17 at 13:45
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The speed relative to Earth is greater than the speed of light. This is consistent with Relativity as the space between us and the distant galaxies has stretched.

The speed is given by

$$(\mathrm{Hubble\ constant}) \times (\mathrm{radius\ of\ the\ observable\ universe\ in\ Mpc})$$

Which, as noted by Pela in a comment, is roughly 3.3 times the speed of light.

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The most distant galaxy currently known is at a redshift $Z=11.1$ (Oesch et al. 2016). According to Ned Wright's cosmology calculator, for a set of concordance cosmological parameters, this corresponds to a comoving distance of 9.88 Gpc (32 billion light years) and a recession velocity (now) from Hubble's law of 2.28c (i.e. 684,000 km/s).

Of course galaxies could exist at greater distances, although they do need time to form after the big bang. Theoretical simulations (e.g. Bromm 2011) suggest star forming galaxies might be present at redshifts of 20, only 200 million years after the big bang. Such galaxies, if they exist, would have recession velocities of 2.5c. This is the maximum possible recession velocity for any galaxy that is observable by us now (or in the near future).

There is no possibility of observable galaxies having recession velocities as high as 3.3c, since that would place them at redshifts of $>1000$ and they would need to have formed even before the epoch of hydrogen recombination.

However, as Pela and Zephyr are pointing out, there are (likely) galaxies that exist now, but that we cannot observe now and never will be able to measure, that are more distant than this and which are receding faster. We are reasonably sure that the universe probed by current observations of the cosmic microwave background is isotropic to comoving distances of about 14.1 Gpc (46 billion light years; "the edge of the observable universe"). Thus galaxies that are currently there, but which are just perturbations in the CMB as we see them now, will have recession velocities of 3.3c. Equally, there could be more distant galaxies than that in a much larger, or possibly infinite, universe and these could have much larger recession velocities still (that we also cannot observe or measure), and indeed they, like the galaxies we do observe, are possibly accelerating away from us.

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  • $\begingroup$ The question doesn't necessarily ask about galaxies known to or observed by us. As pela stated, there are certainly going to be galaxies at the edge of the observable universe which we are not observable in their present state, but they still almost assuredly exist and are receding from us. $\endgroup$ – zephyr Jun 20 '17 at 12:57
  • $\begingroup$ @Zephyr But then what is special about the edge of the observable universe? Galaxies will (probably) exist beyond this and have even faster recession velocities. I have struggled to edit my answer to make your point, but I'm not entirely sure what it is. 3.3c is the recession velocity of the cosmic microwave background. $\endgroup$ – Rob Jeffries Jun 20 '17 at 17:37
  • $\begingroup$ There's nothing special. I was just pointing out that possibly the question is asking about galaxies at the edge of the universe, be they visible or not. I think the question was just, how fast are the fastest things moving away from us (in the observable universe). I guess its all in how you interpret the question. $\endgroup$ – zephyr Jun 20 '17 at 17:53

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