When our entire section of the universe was in a single hot dark dense state, right before our big bang, what was the escape velocity?
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To answer your question, it is worth noting that “escape velocity” is a term frequently used concerning objects within gravitational fields whereby an object opposes the gravitational pull of another. This point (in the case of the Big Bang singularity) represents the whole universe in an extremely dense form rather than a localized field of gravity consisting of distinct objects. Let us also consider the idea of the entire universe as one massive body (even though this is not wholly accurate) for argument's sake, then calculating its escape speed would be meaningless since there is no external field of gravitational force to escape from. The universe would amount to nothing else besides itself and thus cannot have any other thing against which to measure escape velocity. In the context of Big Bang, however, expansion does not need to achieve escape velocity in the usual sense. Instead, it occurs because space itself undergoes a rapid expansion as described by cosmic inflation theory and later by general relativity's description of accelerated expansion of the universe. Thereby, the existence of this expansion does not necessarily imply that universal magnitude has achieved a certain specific rate relative to some kind of external gravitational field but simply indicates that such motion characterizes its structure as it changes over time for all matter-energy with respect to inertia according to fabric physics nature.
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