We have mountains of evidence about singularities and how they work, and we have mountains of evidence that the "Big Bang" was the origin of the universe as we know it. But if compressing enough matter into a small space causes an inescapable singularity (i.e., a black hole), why does compressing all matter into a small space lead to a sudden expansion?
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3"We have mountains of evidence about singularities and how they work" Citation needed? We have a lot of math and the math is grounded in experiment (sometimes subtle and beautiful experiments, too), but we don't have singularities to do experiments on. – dmckee --- ex-moderator kitten Feb 11 '15 at 14:57
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You don't have a singularity just lying around? Get with the times :P Seriously though, what I meant was we have done so many experiments and made so many observations, that the existence of singularities isn't really disputed despite us not having directly observed one (that I know of). – thanby Feb 11 '15 at 15:22
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2I would say the actual existence of singularities is pretty far from established :) It's a sign that the equations break down, that's about as far as the "not disputed" goes I think. – BjornW Feb 11 '15 at 16:46
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3The Big Bang didn't happen at a point. It is very different from the singularity in a black hole. – John Rennie Feb 11 '15 at 16:58
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1possible duplicate of Big Bang snuffed by a black hole? – John Rennie Feb 11 '15 at 16:59
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It seems that the answer to my question is that there's a difference between the pre-inflation universe "singularity" and that of other types of singularities like a black hole. It wasn't a singularity as describes a black hole, it was a point in time where the scale of the universe was zero. All that exists didn't occupy a single point in space in the way matter collapses into a singularity in the universe we know, and the density of the universe was still homogenous. But the scale of it was reduced so much that the distance between everything was essentially zero, despite being an infinite universe, hence the big bang "happening everywhere at once" instead of at what we consider in our narrow view to be a single point.
As pointed out in the comments, this question has a very good explanation of how that works.
Edited with corrections suggested in the comments, thanks!
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2The Big Bang is definitely a singularity. However there are many different types of singularity. The singularity at the centre of a black hole is just one type. – John Rennie Feb 12 '15 at 11:26
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The "explosion" wasn't caused by matter being under high pressure. It is thought that during the first few moments after the creation of the Universe, it went through a phase called "inflation", where there was no matter or radiation or anything else, only potential energy, which lasted $\sim10^{-34}$–$10^{-32}$ seconds and blew space up by a factor of at least $e^{60}$. See e.g. this post for more on inflation. When inflation ended, the Universe continued to expand but slowly decelerated due to the gravitational attraction of its matter. Recently, though, it started accelerating again due to something called dark energy.
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So if I'm understanding you correctly, the "singularity" state of the universe pre-inflation is not at all the same thing as the singularity of a black hole? If so, what is the difference? – thanby Feb 11 '15 at 15:30
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1Well, its the same in the sense that both mark a breakdown of our understanding of the physics governing it, since their mathematical description contain infinite densities, which probably doesn't make sense physically. This may be "saved" by quantum mechanics (QM), since there exists a lower, non-zero limit to physical distances, but reconciling QM and gravity isn't yet successful. But actually, I think your own answer nails it; there is a difference in that the black hole singularity is a point in space, whereas the Big Bang singularity is all of space itself. +1 for that! – pela Feb 11 '15 at 21:14