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Ok, as I understand the expansion of the initial singularity was caused by quantum fluctuations like the ones predicted by the Heisenberg Uncertainty Principle. But how can these fluctuations occur within a singularity? And how can they cause the expansion of that singularity? Or do I have a terrible misunderstanding of the theory?

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    $\begingroup$ This questions most definitely pushes the boundaries of our understanding of Cosmology. As of now, there is now concise and agreed upon answer. I'll see if I can't find the most promising theories, and give you a short breakdown on each. $\endgroup$ – Doryan Miller Jul 12 '14 at 20:13
  • $\begingroup$ @DoryanMiller meant ''... no concise and agrees upon answer''. AND ''... see if I can find the most ...'' . The current sentence means exactly opposite of what was probably intended. :) $\endgroup$ – 299792458 Jul 13 '14 at 6:03
  • $\begingroup$ By most agreed upon, I mean the theories with the most support by whatever means. (I would assume observational evidence.) $\endgroup$ – Doryan Miller Jul 13 '14 at 8:28
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Let's start by setting the scene. We've got a hyperdense (understatement) singularity containing everything at $t = 0$. This is the beginning of time. Right now, we have no reason to assume that anything existed before then. Asking what happened before the Big-Bang ( depending on which model you use ) is not something that one can ask since we assume nothing existed prior. This is a boundary of Physics. The origin of the universe will determine it's future shape. We turn our study to the shape, as we can attempt to measure now, to gain information regarding the former.

The Friedmann Closed 3-Sphere is one example of a space-time geometry that could be occurring. In this model, the universe can be viewed as a football (American) shaped entity basically. If you set it up as you would for someone about to kick the ball, the bottom tip corresponds to the Big Bang singularity, $t=0$. The surface of the ball is the Universe. Ignore the space in and around the ball. Trace up the surface to the other tip, and you have a worldline. If you notice, all of spacetime starts small, then as time presses on, it expands to a maximum ( max radius of the football ) and then begins to shrink back down to a point ( the other tip ). This is the Big-Crunch model.

Other Scientists then posed the question, "What if the end is the beginning?" What if the singularity that the Universe ended in, is the same singularity that the Universe started in? This leads to an oscillating Universe. It looks like one just stacked footballs on top of each other lengthwise, and time progression can be taken to be upwards. Conversely, you can just plot $\sin{t}$ against $-\sin{t}$ enter image description here, and the difference between these at any $t$ is the radius of the universe. If you look at the zeroes of that function, you notice there are an infinite number of zeroes that look like big crunches for increasing $t$, and big bangs for decreasing $t$. This model however doesn't tell us where we are in that cycle. Arguably it doesn't matter if the Universe oscillates in that fashion. We could find all the answers we wanted approaching a big crunch era.

A Universe with a cosmological constant, $\Lambda$, and nothing else results in what we call de Sitter Spacetime. It looks like this. Where time flows upwards, and again, spacetime itself is the surface of the hyperboloid. adS Space This shape, as you can see, starts off at infinite size, infinitely long ago, then contracts to a minimum size, and begins to expand back into infinity. This model is very similar to the oscillating universe.

One of the more interesting models is the adS Bubble Universe. This model is the direct result of quantum fluctuations in a high-density, inflationary vacuum, which causes a bubble from the de Sitter waist to form, having non zero size. The walls of the de Sitter space, however, are expanding faster and faster, with the whole of the Universe getting bigger and bigger, but the bubble that arose from quantum fluctuations is getting bigger too. The walls of adS space had a head start, so we have a bubble in a cone shaped Universe. If the bubble however is inflating just like the adS space it's in, why should not the inside of the bubble be an entire inflationary Universe just like the one we observe? This lead to a version of the multiverse.

I could go on forever regarding the possibilities that we have, but I think you probably get the point by now. You seem to have an interest in the field of Cosmology, which largely deals with the origin, evolution, and fate of the Universe. I suggest you read up on it! It's an awesome subject. The reference I used to answer this question is a rather interesting book called Time Travel In Einstein's Universe by J. Richard Gott. Although the book is geared towards the intricacies of time travel, the section on Cosmology is pretty thorough.

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  • $\begingroup$ "We've got a hyperdense (understatement) point containing everything at t=0" Saying "point" here is a little misleading, especially given the common misconceptions surrounding this question. It's better to speak of a singularity in your model. $\endgroup$ – ticster Jul 12 '14 at 21:05
  • $\begingroup$ Fair enough. Editing. But in what way do you find it misleading? $\endgroup$ – Doryan Miller Jul 12 '14 at 21:06
  • $\begingroup$ I've often encountered laymen who hear "point" and think it means all matter was balled up into a point and then it exploded, or at best that the actual shape of the universe at the time can be described as a point, but then wonder how this turns into a (in)finite space. While the latter is not as wrong as the former, it's still not right. It's better to present it the situation as it is : if we extrapolate say a flat FLRW metric backwards in time, the scale factor reaches 0 at a finite point in time. This is different from just saying "it's a point" in ways I'm sure I don't have to explain. $\endgroup$ – ticster Jul 12 '14 at 21:14
  • $\begingroup$ I'd never heard the whole point-singularity idea explained in terms of the scale factor. I've always just had sort of an intrinsic understanding of the idea. That's good to know, and makes a ton of sense! ( I've restrained myself from pushing into the mathematics of cosmology until I get to it in Leonard Susskind's Theoretical Minimum ) $\endgroup$ – Doryan Miller Jul 12 '14 at 22:12
  • $\begingroup$ Deriving the Friedmann equations is one of the simplest things you can do with GR (so still not totally trivial, but something you can teach yourself online, at least to a somewhat satisfactory level). I'd recommend doing it. Cosmology is quite beautiful in its simplicity, and the various models thrown around (and in particular their motivations) becomes immediately clearer. $\endgroup$ – ticster Jul 12 '14 at 22:19

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