Questions regarding the currently prevalent cosmological model for the origin of the universe.

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How do we know the big bang expanded space and not the other way around?

Whenever we hear an explanation about the big bang, it is always phrased in such a way that it was an explosion which used some kind of pressure to expanded the universe out. I wonder, however, would ...
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How was all the matter curled up inside a singularity during big bang ?

If the singularity had infinite mass, temperature and density, then it should curve space and time but there was no space-time before big bang. So where did the singularity come to existence without ...