Understanding the cause of the big bang 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? 
 A: 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 $-\sin{t}$ , 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.  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.
