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When I hear about the most distant objects in the universe, such as the recently discovered galaxy GN-z11, their distances are usually stated to be a little under 14 billion light years away....

But, the observable universe is 46.5 billion light years in radius... So..

Does the 13.4 billion light years or so distance for GN-z11 factor out the expansion of the universe itself? So-called 'co-moving distance'? Or is it actually, currently about 13.4 billion light years away?

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According to Wikipedia, GN-z11 has a redshift of 11.09, which, according to Ned Wright's cosmology calculator, corresponds to a light travel time of about 13 billion years and a comoving radial distance of about 32 billion light years.

The comoving radial distance is the distance measure with respect to which the diameter of the observable universe is about 46 billion light years, so that's the one you want in this context.

A lot of people don't understand the implications of cosmological expansion and think that if the light travel time is 13 billion years, then the distance to the galaxy must be (or must have been) 13 billion light years. They're sure enough of it that they'll report that distance as fact, without disclosing that they calculated it themselves. As a result, distances in popular articles generally can't be trusted. You can trust the redshift if it's reported, and you can probably trust times (either light travel time or time since the big bang).

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