Implications of a closed universe and recollapse

In summary, a closed universe with a density parameter greater than 1 will eventually recollapse upon itself. The expansion of the universe is not about matter flying apart, but about the geometry of spacetime. As the universe collapses, the hypersphere itself would get smaller and smaller. However, the exact outcome and whether one could see the back of their own head before the collapse is uncertain and depends on the content of the universe. A universe with a large cosmological constant would undergo accelerated expansion, driving it closer to a density parameter of 1 and potentially morphing it into a flat, infinite universe. However, this scenario would not be possible in our current universe with a small cosmological constant.
Summary: Looking for detail about what the recollapse of a closed universe would entail

As I understand it, in a universe in which the density parameter is greater than 1, a closed universe, everything would eventually recollapse upon itself. My question is: does this recollapse just refer to all the matter falling back together again, or would the geometric confines of the universe itself get closer and closer together and ultimately disappear?

If we imagine the closed universe as a hypersphere with 3d space curving back on itself, I think it's correct to say if you flew a spaceship in a single direction for an immensely long time you would end up back where you started, right? So does that mean that as the universe collapses, the distance it takes to loop back in on your starting location would lessen? And eventually as the collapse of the universe is about to complete, you could see the back of your own head by staring straight ahead?

As I understand it, in a universe in which the density parameter is greater than 1, a closed universe, everything would eventually recollapse upon itself.
This is not entirely true. It depends on the type of energy content in the universe in question. For example, a universe with a sufficiently large cosmological constant will undergo accelerated expansion even if the density is larger than one (which, of course, will drive the universe closer and closer to a density parameter of 1).

My question is: does this recollapse just refer to all the matter falling back together again, or would the geometric confines of the universe itself get closer and closer together and ultimately disappear?
The expansion of the universe is not about the matter flying apart. It is about the geometry of spacetime. This would also be true in the case of a contracting universe. Hence, the hypersphere itself would get smaller and smaller.

And eventually as the collapse of the universe is about to complete, you could see the back of your own head by staring straight ahead?
This would not be certain either, you would have to do the maths. The problem is that the universe might fully collapse before you see the back of your head. It depends on when the signal is sent out as well as on the exact content of the universe (which ties into how the contraction of the scale factor occurs).

Orodruin said:
a universe with a sufficiently large cosmological constant will undergo accelerated expansion even if the density is larger than one (which, of course, will drive the universe closer and closer to a density parameter of 1).
So, the universe could be a hypersphere and yet still rapidly expanding in 5D because of dark energy? And then that expansion could drive the universe down to a density parameter of 1, and the hypersphere would morph ('pop?') into a flat universe, functionally infinite in scope? I didn't realize that the density parameter could change over time

It sounds like it's almost certain that the universe will end up 'flat' and infinite. Because even if it's a hypersphere at the moment it'll eventually drive itself to omega=1.

I'm trying to write a hard sci-fi book about an extremely advanced civilization dealing with the end of its universe. Initially I was going to write about a universe in which heat-death had occurred and the temperature was nearing absolute zero. But then I got the idea of writing instead about a closed universe that was collapsing and would soon disappear entirely. The idea of all of 3d space becoming smaller and smaller and eventually ceasing to exist seems more cosmologically terrifying to me.

I really like the idea of writing about a hyperspherical universe that is finite but unbounded, but if it doesn't square with our current knowledge about physics I'll have to go with the flat universe nearing heat-death. Thoughts/advice?

So, the universe could be a hypersphere and yet still rapidly expanding in 5D because of dark energy?
There is no fifth dimension here. Spacetime is 4-dimensional. There is no need for an embedding space.

And then that expansion could drive the universe down to a density parameter of 1, and the hypersphere would morph ('pop?') into a flat universe, functionally infinite in scope?
No. As the universe expands it becomes closer and closer to being flat in that scenario. It never becomes flat.
Also note that we are talking about a universe with a significant cosmological constant.

I really like the idea of writing about a hyperspherical universe that is finite but unbounded, but if it doesn't square with our current knowledge about physics I'll have to go with the flat universe nearing heat-death. Thoughts/advice?
You can imagine such a Universe as I said. It just cannot have a significant cosmological constant. It will also not be our universe since we have a significant amount of dark energy. Anyway, it is your story.

[...snip...]

I'm trying to write a hard sci-fi book about an extremely advanced civilization dealing with the end of its universe. Initially I was going to write about a universe in which heat-death had occurred and the temperature was nearing absolute zero. But then I got the idea of writing instead about a closed universe that was collapsing and would soon disappear entirely. The idea of all of 3d space becoming smaller and smaller and eventually ceasing to exist seems more cosmologically terrifying to me.

I really like the idea of writing about a hyperspherical universe that is finite but unbounded, but if it doesn't square with our current knowledge about physics I'll have to go with the flat universe nearing heat-death. Thoughts/advice?
You enjoy an enviable position as an author in having multiple fictional outcomes for your decadent universes. Use both ideas.

Establish a universe in your preferred set. Establish dedicated aware science-oriented characters who understand the nature of their existence but who are unwilling to go 'quietly into the dark night'. When things appear darkest, a strange communication arrives.

Could humans living in a universe under a different parameter set be trying to survive? Perhaps the scientists in a "closed shrinking" universe learn how to send/receive information to the "open expanding" characters. Can they save each other?

1. What is a closed universe?

A closed universe is a hypothetical model of the universe where the total amount of matter and energy is enough to eventually halt the expansion of the universe and cause it to recollapse.

2. How does a closed universe differ from an open universe?

An open universe is a model where the expansion of the universe continues indefinitely, while a closed universe eventually reaches a maximum size and then contracts.

3. What are the implications of a closed universe?

The implications of a closed universe include the possibility of a finite lifespan for the universe, as well as the potential for a "big crunch" scenario where all matter and energy in the universe is compressed into a single point.

4. Is there evidence for a closed universe?

Currently, there is no definitive evidence for a closed universe. However, some cosmological models and observations suggest that the universe may have enough matter and energy to eventually recollapse.

5. What would happen if the universe recollapsed?

If the universe were to recollapse, it would result in a massive release of energy and potentially lead to the formation of a new universe in a cyclical process known as the "Big Bounce."

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