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There is an event horizon where cosmic expansion leads to superluminal recession speeds for sufficiently distant objects -- the Hubble Volume.

1) Does matter beyond the event horizon affect us gravitationally or otherwise?

If the answer is no, there is a follow-up question.

If everything beyond this horizon is causally disconnected, it gives rise to the possibility that the universe is arbitrarily large, and undetectably so...

If the distribution of matter is random then although it is locally smooth, in a sufficiently large universe there may be large regions on the thin tail of the bell curve which are relatively empty or relatively full...

We've all seen that chart of possible Hubble constants: <1 means big crunch, >1 means heat death, =1 means asymptotic growth. We've all seen that the constant appears to be very, very close to 1...

Putting all this together...

2) Could we have a situation in which two relatively dense regions of the universe, separated by a sparse region, expand away from one another faster than the average rate due to weaker attraction locally, and so end up causally separated beyond the event horizon of expansion, while within each region there is a local big crunch?

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Leaving aside for the moment the dark energy and cosmic acceleration, there isn't an event horizon 13.7 billion light years away. It's true that we can't see farther than this at the moment, but we can do if we simply wait. Every year we can can see one light year farther. The reason that dark energy complicates this is that the acceleration caused by dark energy does create a true event horizon just like the one around a black hole, and indeed it Hawking radiates just like a black hole horizon. However this horizon is currently too far away for us to see. I forget the exact distance, but it's farther than 13.7 Glyears and none of us will live to see it.

Anyhow, matter farther than 13.7 Glyears away hasn't influenced us yet, but it will do if we wait a while.

But to get to your question, it's entirely possible that there are density fluctuations on a scale greater than 13.7 Glyears. In fact this was suggested as an origin for the cosmic acceleration i.e. it could simply be that we are at the centre of an underdense region so our vicinity is expanding faster than the average. I don't think many people believe this to be likely because we'd need to be smack in the centre, which seems an unlikely coincidence, and in any case there is other evidence for the dark energy.

The CMB shows no signs of large scale overdense regions, but they could exist on a scale much larger than 13.7 Glyears, and dark energy permitting they could collapse to form a locally overdense region. This wouldn't be a big crunch though - at best they'd form dense galaxy clusters and if you wait a very very long time an extremely large black hole.

But since there's no evidence for anything like this, the natural assumption is that the universe is uniform on the 13.7 Glyear scale. To assume otherwise seems to be multiplying entities beyond necessity.

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  • $\begingroup$ PS re the horizon, arxiv.org/abs/astro-ph/0310808 might be of interest $\endgroup$
    – John Rennie
    Commented Jun 25, 2012 at 17:38
  • $\begingroup$ I'm talking about an event horizon formed by cosmic expansion creating superluminal velocities for sufficiently-separate particles, not just the age-of-the-universe-times-c boundry. Assuming nonuniform distributions isn't multiplying entities: if you toss a coin enough times eventually you'll get a billion heads, so a 1,000,000,000,000,000,000-Glyear universe might contain a 13Glyear region of abnormally low/hight density. $\endgroup$
    – spraff
    Commented Jun 27, 2012 at 10:05
  • $\begingroup$ Yes, a 1,000,000,000,000,000,000-Glyear universe would almost certainly contain a 13Glyear region of greater or lower than average density, but I'm not sure what significance this has. The universe is only 13.7 Gyears old, and it's very unlikely it currently contains a 13Glyear region of greater or lower than average density, even though it's probably infinite. $\endgroup$
    – John Rennie
    Commented Jun 27, 2012 at 10:31
  • $\begingroup$ The significance is that the rate of expansion would be slower in one region than another, so if the overall Hubble constant is pretty much exactly 1, then one region would be <1 and another >1, and this could lead to a causal partition of the universe if the regions were far enough apart that they were separating faster than c -- having separate big crunches. Or if not, why not? That's the question. $\endgroup$
    – spraff
    Commented Jun 28, 2012 at 8:35
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    $\begingroup$ This answer is sort of correct, but the cosmological horizon is not that far from a black hole horizon even now, and it is wrong to place the horizon of the CC outside of it. $\endgroup$
    – Ron Maimon
    Commented Jul 17, 2012 at 16:52

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