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Suppose that we have a particle moving at $0.8 c$ (or even a photon) and it is just, say $2 \times 10^{5} m$ away from the boundary of the universe (whatever that boundary be).

Since the expansion speed of universe is less than that of our particle then it has to reach the boundary (right?), what happens then? Does it bound back? Does it continue to be on the boundary?

Qmechanic
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self.grassmanian
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    In mainstream physics the universe has no boundary. – G. Smith Jul 26 '20 at 04:09
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    I agree that in standard LambdaCDM the Universe doesn't have a boundary. But, in my opinion, it would be a mistake to close this question on these grounds. It's certainly possible to consider spacetimes with boundaries in General Relativity. Also, there are published analyses of CMB data that search for non-trivial topology -- while this isn't a boundary, it can be viewed as a non-trivial boundary condition. Anyway, just my 2 cents. – Andrew Jul 26 '20 at 04:42
  • @Andrew Can you please say how expansion of universe is factored in LambdaCDM? Just as an expansion between two points in vacuum? It is based on Big Bang Cosmology, right? Then it does appear that there is a boundary (as a bubble expanding). – self.grassmanian Jul 26 '20 at 04:52
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    @asymptoticallyboundedgluon There is a stack exchange question addressing this: https://physics.stackexchange.com/questions/136860/did-the-big-bang-happen-at-a-point. Basically, LambdaCDM is a specific example of a big bang cosmology. There is no (space-like) boundary, since the big bang happened "everywhere". – Andrew Jul 26 '20 at 04:56
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    As regards the votes to close for not being "mainstream" - There seems to be a difference between a misunderstanding of mainstream physics and something that's not mainstream. I read this as the former and am voting to leave open. – Brick Jul 27 '20 at 13:43

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As far as we know, the Universe does not have a boundary. But, if it does, then we will need to know what are the boundary conditions in order to answer your question of what a particle will do when it reaches it. For example...

  • The Universe could have reflecting boundary conditions, in which case the photon would bounce back from the boundary.
  • The Universe could have transmitting boundary conditions, in which case the photon would leave the Universe forever.
  • The Universe could have periodic boundary conditions, in which case the photon will effectively "circle around" the Universe.

Other boundary conditions are possible as well.

I would personally find the first two options are very weird, and the last one possible but also somewhat unexpected. But, this maybe just shows my own biases.

Andrew
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    Thanks. It is interesting that my first thought for what happens was "circle around" as you put it. I thought it too weird and did not mention! – self.grassmanian Jul 26 '20 at 04:15
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    There are actually some papers which look at this possibility, for example: https://arxiv.org/abs/1206.2939 – Andrew Jul 26 '20 at 04:23
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    @asymptoticallyboundedgluon In a Friedmann universe with positive spatial curvature, you can “circle around” but this has nothing to do with any boundary. – G. Smith Jul 26 '20 at 04:37