The accelerating expansion of space means that the space between us and far away galaxies expands faster than light can travel through space. There is a horizon of possible observation beyond which galaxies disappear from us.

At what rate do galaxies, or some other measurement of mass/energy, disappear beyond that horizon at present rate? Will future telescopes actually see galaxies red shift themselves into oblivion? I imagine there being issues about the definitions of "when" and "where" in this context. Answers should try to address how they deal with that.

Since the radius of the observable universe expands at the speed of light, my intuition tells me that there should've been a point in time when the expansion of space balanced the arrival of light of more distant parts of space. if so, when did that happen?


1 Answer 1


This is a tricky question to answer, because it has some false and imprecise assumptions baked into it. The short version is: I don't know at what rate stuff is currently crossing the cosmic Event Horizon. But future telescopes will not see these galaxies redshift themselves into oblivion, because this will happen in the infinitely far future, literally. Cosmological redshift is equivalent to relativistic time dilation; events that are redshifted from our point of view also play out slower, and infinite redshift means they come to a complete halt.

It is also not correct that the radius of the observable Universe is expanding at the speed of light. There are two different radii that could be candidates for the title "limit of the observable Universe"; they are very different but both expand faster than light.

Your intuition is right, however, that the distance at which galaxies recede from us at exactly light speed - the one we call the Hubble Sphere - has been expanding and since approaching us again. It reached its maximum when the cosmic expansion went from decelerating to accelerating, when the Universe was around half its current age. The Hubble Sphere, however, is not the limit of anything.

One of the two horizons, the one that seems to be the one you have in mind in the beeginning of your question, is the Event Horizon. This is the current distance, beyond which light emitted at this cosmological time will never have the chance to reach us. This horizon receding from us in proper distance, and since it is located outside the Hubble Sphere, these regions of Space are actually receding from us faster than light. In co-moving coordinates, the event horizon is approaching us. Co-moving coordinates is a coordinate system that stretches along with the expansion of the Universe, such that a galaxy that is not influenced by anything else than cosmic expansion will have constant coordinates in time. Because the cosmological expansion is accelerating, it gets harder and harder for light at a fixed co-moving distance to reach us until it gets impossible and the Galaxy redshifts to infinity. This is equivalent to saying that the Event Horizon has moved inwards past this galaxy in co-moving coordinates. In proper coordinates, it amounts to saying that the galaxy overtakes the Event Horizon. Ours, by the way, is currently at a redshift of around 2, around 18 billion light years away. The light we receive from this distance is only slightly redshifted now, but the light that is emitted now will be redshifted to infinity when it reaches us at infinite time.

There is also another horizon, however, which does expand forever, also in co-moving coordinates. That is the current co-moving distance at which light emitted at the time of Big Bang reaches us just now. In co-moving coordinates, this horizon expands slower and slower, which is why the CMB gets more and more redshifted. Objects currently on the Particle Horizon are a long time out of our Event Horizon - we can only ever see the very beginning of their history, before they redshift into oblivion. And the objects shifting into our particle horizon will show us still less of their history before having left the Event Horizon for good (yes, language gets hairy when talking relativistic time).

So it is hard say what the limit of the observable Universe is, it is simply not well defined. The Event Horizon has always been growing in proper distance but shrinking in co-moving distance. The Particle Horizon has always been growing both in co+moving and proper distance. The Event Horizon has always been expanding faster than light, and always will. The particle horizon started out slower, but very soon overtook lightspeed in expansion velocity.

Interestingly, all objects with a redshift higher than $z \sim 1.5$ are not just receding faster than light, but they always have been! Yet we observe them with no trouble.

  • $\begingroup$ I believe, the question was about galaxies "crossing" Event Horizon in co-moving coordinates, most likely questioning if we have any observable proofs that EH does actually exist. $\endgroup$ Commented Apr 17, 2018 at 10:54

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