I'll try to give the "Cliff-notes" version:
First, gravitational fields have a negative energy associated with them; the stronger the field, the greater the negative energy ("Physicist" can give you an example which illustrates that gravitational fields have negative energy.)
Whatever matter/energy existed immediately after the BB took place has some gravitational field(s) associated with it. The Inflation phase creates new space that wasn't there before (again, see "Physicist" for an explanation of the mechanism by which the rapid expansion of space occurs).
Now, for the really cool part: whenever new space is created, it gets permeated by the existing gravitational fields, which means the negative energy associated with those fields is decreasing (meaning increasing negatively). But the Law of Conservation of Energy says you can't create (or destroy) energy like that, so something has to happen to balance the energy equation so that the net result is zero energy change. That mechanism is the creation of new matter/energy in the newly created space! And the really cool thing is that the Conservation of Energy requirement means that the quantity of new matter/energy being created is EXACTLY equal to the negative energy of the gravitational fields! This means that as the Universe Inflated, the end result HAS TO BE a Universe in which the matter density is equal to the "critical" value at which the energy of the gravitation fields is counterbalanced by the positive matter/energy in the Universe.
IOW, the "perfect balance" isn't a case of extraordinary "fine tuning" or dumb luck, but rather is a consequence of one of the most basic Laws of Physics, the Conservation of Energy. The Universe had no choice but to turn out this way.
[Another geek alert]: Conservation of Energy is intimately connected with a fundamental feature of the Universe, by way of Noether's Theorem. Energy is conserved iff the rules of physics are invariant under continuous temporal transformation, which is true iff the Universe is temporally homogeneous. Similar relations exist for Conservation of momentum, and angular momentum, which relate respectively to the spatial homogeneity and isotropy of the Universe.
Or so I understand....
Prior to t=0 the Laws of Physics were already firmly in place?
Doesn't gravity travel at the speed of light?