[neutralino]

Originally Posted by Profpat GIVEN: By extrapolating this expansion back in time, one approaches a gravitational singularity where everything in the universe was compressed into an infinitesimal point; an abstract mathematical concept that may or may not correspond to reality.

It is conjectured (well, it's more than a conjecture) that, in a working theory of quantum gravity, there will be no initial singularity. As you say, a singularity is a mathematical concept; it basically means that there are some infinities in the theory at that point which says that the theory is not valid there. Now, some infinities are easy to iron out (QED, for example), but it turns out that, when trying to couple gravity to quantum field theory, the infinities will just not go! So, we do not know how the gravitational force couples with the others.

This idea gave rise to the Big Bang Theory, the dominant model in cosmology today.

Now, we should be more precise, and say that the big bang theory only says the content of the universe was once much more dense than it is today. Cosmologists try and run the clock back as far as it'll go, but, using the standard model of cosmology (which is called Lambda CDM-- lambda indicating the need for a cosmological constant, or dark energy, and CDM standing for cold dark matter) we can only run the clock back to a fraction of a second after the big bang. This is due to the fact that, on small scales, quantum effects will greatly outweigh gravitational effects. However, since noone knows how to couple gravity and quantum field theory, we do not know how or when these quantum effects outweigh gravity.

The important point to notice is that the standard model of cosmology does not state that universe expanded from a single point.