> I got the impression
> that during the very early Big Bang, everything was within everything
> else's light cone.
Not in standard Big Bang cosmology, and hence the "horizon problem" -- how to explain why distant regions of the universe are in thermal equilibrium despite them never having been in causal contact. Inflation theory tries to solve this problem by postulating an epoch of very rapid expansion in the early universe, so that all that we see when we look around in cosmos today originated from such a small volume that within that volume things had had time to interact before the inflation set in.
> Of course, that doesn't mean an infinite number of
> actions could be performed. What's the function for the radius of the
> Big Bang as a function of time? Anyone know?
It depends on the global topology of the universe. If the universe is closed then when it is radiation dominated (as it was in its early stages) it expands as
R = sqrt[A^2 + t^2], where t is a time parameter -A<t<+A.
If open, then
R = sqrt[t^2 - A^2], where +A<t<positive infinity
(Note that in the latter case, R is not a radius -- the universe is spatially infinite at all times -- but a scale factor.)
Finally, if the universe is flat, then
R = sqrt[2At], 0<t< positive infinity
where again R is a scale factor.
Nick Bostrom
http://www.hedweb.com/nickb n.bostrom@lse.ac.uk
Department of Philosophy, Logic and Scientific Method
London School of Economics