What's the evidence supporting 1 singular Big Bang? 
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What has been proved about the big bang, and what has not? 

I love to dabble with science, I'm by no means a scolar in this field. One thing that haven't seen proven yet (maybe I missed it) is that there was only 1 singular Big Bang where it all started. 
As I understand, when Hubble discovered that the universe was expanding, the conclusion was also that it was much smaller in the past. That I follow, but the theories seem to automatically agree on there being 1 Big Bang where everything started. 
Couldn't there have been multiple points where matter etc 'flipped' into existence roughly around the same place and time? Is there any evidence for that? Does all the red shift for instance point to 1 spot? 
Thanks for your time and knowledge in advance,
Gert-Jan
 A: I've answered a series of related questions recently. Do a search of the site for "FLRW metric" to find relevant questions.
Anyhow, the idea of the Big Bang arose from a solution to the Einstein equations called the FLRW metric. If you assume that the universe is homogenous and isotropic (i.e. that it's basically the same everywhere) then you can solve the Einstein equation to give an equation that describes how the universe expands. This solution is called the FLRW metric, and it does seem to be a very good description of the universe as we see it today.
If you take the FLRW description of the universe and you wind time backwards, then as you approach 13.7 billion years ago the density becomes greater and greater and eventually becomes infinite. This point is known as the Big Bang. The Big Bang happens at the same time everywhere. Actually, at the moment of the Big Bang the FLRW metric predicts that the spacing between any two points falls to zero, but the universe remains infinite. This paradoxical situation is why most of think that some theory of quantum gravity will cut in before we reach the Big Bang.
So, to answer your question, the universe today seems to be well described by the FLRW metric, and the FLRW metric predicts that the Big Bang happened everywhere at the same time. To answer your specific question about the red shift, the red shift appears to be the same in all directions so this supports an isotropic universe and a single Big Bang everywhere.
It's possible that our interpretation of the experimental evidence might change as we learn more. For example you might like to have a look at this question, which discusses eternal inflation and the possibility that the Big Bang is different in different parts of the universe. At the moment there is no experimental evidence to support the idea of eternal inflation.
A: It is an explainable confusion when one thinks that the Big Bang happened at one point in space, to extend it to many points in space. But, the Big Bang happened in space time, i.e. in four dimensions, and that one singularity is at the (0,0,0,0) origin of all the space points in all the observable universe. The first  figure shows the balloon analogy, how all the points in a two dimensional surface recede from each other and all start at the origin.
