# Observable universe at $t=$infinity

On researching about observable universe I came across this excellent answer that explained Comoving vs Proper distance: https://physics.stackexchange.com/a/401181/281013

It answered why the edge of present observable universe is objects that are at proper distance <= 46.5 billion light yrs from us presently (even though the universe is 13.8 billion light yrs old). It also explained at t=infinity, the edge of our observable universe will max out at objects that are 62 billion light yrs from us presently.

Any object that is presently >62 billion light yrs away from us will never be visible to us. Ever.

While that itself is a bleak thought (since it raises so many questions around observable universe vs actual (or total) universe and the natural limit that fact will pose on our ability to truly understand the universe fully when we aren’t even seeing ‘everything’ in the universe presently, nor will we ever see in the future. (This is of course assuming we will be staying within the Milky Way by figuring out inter-stellar travel within our galaxy after our sun burns out, but wouldn’t figure out a way for inter-galactic travel via wormholes or something else to the get to the edge of the observable universe somehow.. which we very well could.. so maybe no need to be pessimistic 😊).

Keeping that aside, my question was, that answer as laid out by Pulsar seemed to imply that our particle horizon will be an ever expanding sphere which will max out at radius of 62 billion light yrs. However, my understanding is since the expansion of universe is accelerating, in our ultimate future there will be nothing left in observable universe except the milky way galaxy (and probably the local cluster) since the space that encapsulates all other (even relatively nearby) galaxies would have accelerated by then to be expanding greater than c. And light of even those nearby galaxies that we can see today will no longer be able to reach us.

So how do I square the fact that the observable universe will shrink over time with what the article seemed to suggest that the observable universe will grow over time? Surely I’m missing something.

Any help will be appreciated. I’m new to Stack Exchange so couldn’t post a comment on that thread (need 50 points I guess), hence posing it as a question.

• The answer depends on how do you define "the observable universe will shrink/grow": by distance or by stuff within that distance. Given that the universe is in accelerated expansion, in the future you would see less galaxies in total, even though your visible horizon is expanding. Commented Nov 30, 2020 at 17:48
• Thanks for the reply @MadMax. The article implied at t=infinity our event horizon will be all objects that are - today - within a radius of 62 billion light yrs from us. Presently our event horizon is all objects that are today within a radius of 46.5 billion light yrs from us. If you look at the 3rd graph in the article. So wouldn’t there be more objects in the sky in future? The article seems to imply that but i’m not sure. Commented Dec 9, 2020 at 0:23

You confuse the Particle Horizon (PH), which grows over time, with the Cosmic Event Horizon (EH), which shrinks over time in comoving distance.

Our PH is currently at 46.5 Gly from us and will grow up to about 62 Gly in comoving distance. So objects that are presently >62 Gly away from us will never be visible to us. Remember that comoving distance = current proper distance.

Our EH is currently at 16 Gly from us. In a Lambda-CDM universe, it can be shown that the comoving distance to the EH decreases over time while the proper distance increases and asymptotically approaches a constant value EHmax (a de Sitter Event Horizon), as you can see in the graphs in The difference between comoving and proper distances in defining the observable universe

So in the future, as the Observable Universe grows, new OBJECTS will become observable to us.

On the other hand, since the EH shrinks over time in comoving distance, more and more galaxies will come out of our EH. Does this mean that these galaxies will become invisible? NO. It means that no NEW LIGHT emitted by these galaxies (from the moment they cross our EH) will ever reach us. BUT they will remain visible in the future thanks to the light they emitted BEFORE crossing our EH.

To sum up, the EH defines which EVENTS we can see and which we can't (hence the name 'event horizon'). Instead, the PH defines which OBJECTS we can see and which we can't (hence the name 'particle horizon').

However, in the far future, the light from distant sources will be redshifted out detectability. In practice, all astronomers of the far future will see is the local cluster of galaxies sorrounded by an endless void.