>The inflation in the first microseconds of universe that was faster than C refers only to space - not any of the matter or energy?

It refers to space, but that expansion of space also impacts the matter/energy occupying that space. This does mean that said matter/energy would have had a higher relative velocity than the speed of light ... however that is not an issue because the speed of light limit is a local law, meaning that two objects which are essentially adjacent to each other and capable of communicating causally must never have a relative velocity higher than the speed of light, and that local law is still respected by inflation. For objects which are separated by some distance and not capable of directly communicating or affecting each other causally during the period of inflation, there would be no actual way to measure or compare their relative speeds — any signals emitted by one object during inflation wouldn't be able to reach the other object until the period of inflation is over, since the distance between the signal and the distant object would also be increasing faster than light. Quoting from Wikipedia here:

>>In non-inertial frames of reference (gravitationally curved spacetime or accelerated reference frames), the local speed of light is constant and equal to c, but the speed of light along a trajectory of finite length can differ from c, depending on how distances and times are defined.[32]

This is essentially similar to how the law of conservation of energy is also a local law, meaning that localized, pointlike interactions must always conserve energy, but the total energy of a large volume (such as a region of expanding space) can still yield a change in the total energy within that volume.

>The expandsion of space that continues is only faster than C when added up over large distances?

Yes, that's correct. It's technically a misnomer to say that the rate of expansion is "faster than the speed of light" because the rate of expansion is not even a speed to begin with: it is a rate. It doesn't have the correct dimensions/units to be a speed, so comparing it to the speed of light is comparing apples to oranges. Speeds have units of distance/time, while the rate of expansion of the universe has units of 1/time (like Hertz), which is often more convenient to express as units of distance/time/distance (or a "speed per distance"). The Hubble parameter has a value of about 70 (km/s)/Mpc, which means that a galaxy which is 1 Megaparsec away will have a relative speed of approximately 70 km/s. But a galaxy which is 2 Mpc away will have a relative speed that is twice that (140 km/s), and so on. So the relative speed of an object is proportional to its distance in an expanding spacetime. The more distance that is between the two objects, the greater their relative speed will be. With enough distance between them, the relative speed is greater than that of the speed of light ... but then going back to point #1 above, relative speeds greater than the speed of light is only possible for objects with some substantial distance between them. Regardless of the Hubble parameter's actual value, the relative speed of two objects that are close-by always tends toward zero.

>Why do these theories assume the universe originating from a single tiny point? Would the math or evidence be much different if it had instead all originated from the size of a neutron or even a golf ball for example?

General relativity doesn't assume that the universe originated from a single tiny point, rather it derives this conclusion as a consequence of taking the universe's current state and applying the known laws of gravitational physics backwards deterministically to figure out what its past states must have been. When you take our expanding universe and work backwards, it becomes clear that any two distant objects must have been much closer in the far past ... and that if you go far enough into the past, the distance between them becomes arbitrarily small, reaching zero distance in a finite amount of time (elapsed in reverse).

The math/evidence wouldn't be substantially different, because if you work backwards and ask "how would the universe look if you work backwards in time from when it was the size of a neutron or a golf ball" the answer you get from general relativity is unequivocably "it would have been even smaller in the past, and if you go back just a little further into the past, the distance between all objects becomes exactly zero."

Now, it's worth pointing out that using general relativity to work backwards does result in it becoming non-predictive and giving nonsensical, almost certainly unphysical properties as you get closer and closer to that zero point. As you get that much closer, the universe's energy density also grows without bound, asymptotically approaching infinite density ... and we have very good theoretical reasons to expect that there are undiscovered physical processes in play that would have been very important for the universe's earliest dynamics — for example, corrections to general relativity due to any undiscovered quantum nature of gravity, which might prevent reaching a state where the universe is actually singular, with zero size and infinite density. But until we discover said processes/corrections, understand them, and reconcile them with general relativity's naive classical predictions, we won't be able to properly model the universe's behavior in such a state. So the best we can say at the present time is that general relativity seems to work reliably back far enough in time to where the universe was in an extremely condensed state, but prior to that point, we can't truly be certain just what the earliest moments of the universe were like. All we can say is that the observable universe at one time was in an extremely condensed high-density state, and it expanded from there into what it is today.

Hope that makes sense!