Reconciling the age of the universe to time being relative

Related question. If the radius of the universe is something like 45 billion light years, this implies that the universe is expanding faster than the speed of light. If I understand correctly, galaxies are held together by gravity primarily from dark matter. So our galaxy should remain intact, although destroyed several times over from the merging of nearby galaxies.

However, dark energy is the force that is causing the expansion. So at some point, we actually won’t see any other galaxies as they will be too far and fall outside of our “observable” universe. Assuming that life in our galaxy will die from the galactic collisions, isn’t it possible that new sentient beings many billion light years from now will have no idea that other galaxies even exist at all? Their observable universe will only be their galaxy plus a bunch of empty space. And they will truly feel special. Do I have this correct?

The boundary of the observable Universe moves outward with a peculiar speed (i.e. speed in addition to the recessional speed) of c, so new galaxies are always entering. That said after a time, due to Hubble shift, other galaxies become, for practical purposes, unobservable.

Here is a another doodle, similar to the last, based on a Penrose spacetime diagram -though it is more illustrative than precise. The white line is a worldline of a comoving (“maximal time”) observer, the two yellow lines are the boundaries of the observable Universe. In the background I’ve drawn a rough sketch of how 3 galaxies scale on the diagram. Notice how the amount of space increase between galaxies (because of expansion) and also notice how the observable Universe takes in more galaxies over time.

I think what you’re saying is that the volume of space that we can observe over a fixed period of time grows exponentially, relative to the distance away the light source is. While the diagram depicts this, I don’t think that it addresses the question of whether the expansion is fast enough to cause the universe to recede space away from faster than we can add per your diagram.

I read my last post this morning and realized that it might not make sense. I was half asleep. It makes sense that amount of the universe’s volume that we can observe grows every second. However, if faraway galaxies are receding from us faster than the speed of light, at some point their light won’t be able to reach us any more. Is that incorrect? So while new galaxies can regularly enter our observable universe now, even they will disappear eventually, won’t they?

I could try to write an extensive post poorly reinventing the wheel, but instead I’ll just say: this.

That article is about the cosmic event horizon which, as the article mentions, presently encloses a volume that is only 4% of our present observable Universe.

Cosmic event horizon = events happening now we will be able to see in the future (assuming zero peculiar movement)

Particle horizon = events that happened in the past we can see now = observable Universe

In more technical terms, the cosmic event horizon is the boundary at the present cosmological time of past light cone of “us” at the temporal end of the Universe (whether it be in finite or infinite future), whereas the particle horizon is the boundary at the present cosmological time of the future light cone of “us” at the temporal beginning of the Universe.

NB this is all a lot easier to understand once you understand what a Penrose diagram represents.

The doodle I posted is an attempt to represent that the boundary of the observable Universe expands at c.

So at the boundary of the observable Universe galaxies are receding from us at some “speed” x (from memory x is approximately 3c in the standard cosmological model), but the boundary of the observable Universe is receding from us at x+c, therefore no galaxy can ever leave the observable Universe and new galaxies must enter it.

I should of added though,as I pointed out earlier and the article points out, at late times in the Universe other galaxies become* for practical purposes* impossible to observe due to redshift.

Also, JJ, you might enjoy googling on the “big rip.”