A singularity is a region in which the curvature of space-time becomes infinite. But according to standard big bang models, at the initial point (at which T = 0) the pre-expansion space - as miniscule as it was - was filled uniformly with all energy that ever existed or will exist. But if all energy were concentrated into a single point, and simultaneously at every point, how could there be curvature? There would be no gradation of distortion; all of space would be equally curved, and this is equivalent to there being no curvature. This contradicts the idea that the universe was born from a singularity. Equally, what would this curvature be relative to? We can only say that a particular region is distorted because it deviates from the "natural", un-curved state of space-time. Would it not be nonsensical to say that space-time was curved (to an infinite degree) without there being something to compare this curvature to? It would be akin to stating that the universe is rotating to an infinite rate ... relative to what? All frames of reference exist inside that initial, perhaps infinitely small point, and if the entirety of this point is curved to the same degree, how could one say that it is curved at all?