Quick question that I can't find the answer to: Was the gravitational field of the younger, denser universe sufficient to slow time?

Any gravitational potential will slow time as compared to a smaller potential; this is not the same thing as the field strength. (Potential is the depth of the well. Field strength is the slope of the walls)

Well that doesn't exactly answer my question, but I think it moves in the right direction.

 

Given that answer, can we assume that average gravitational potential at any given point in the young universe was greater than today given the greater density of the young universe as compared to the much larger universe today?

I don't know the answer to that. The potential is the energy per unit mass you'd need (in principle) to get an arbitrary distance away from the source of the gravity. That's something you can answer in the context of a known mass distribution (e.g. our potential with respect to the earth), but I don't know how that is applied to the entire universe and with expansion in play, (which doesn't conserve energy if you don't apply it correctly), nor do I have a feel for how the shape of the universe (open vs closed) affects this.

Fair enough.

 

I had been reading some old discussions about relativity and why it is that the universe can be 153 billion light years across and only 14 billion years old. While the argument that it is a matter of expanding space makes perfect sense I had wondered whether time dilation played a part in making initial expansion appear to happen at a rate far faster than the speed of light.

The expansion is always faster than the speed of light, if the two points in question are far enough apart.