I'm guessing I'm correct that relativity states that time slows near a heavier body apparently due to gravity. So time and gravity are somehow linked according to relativity.
More accurately, gravity is a curvature of spacetime. The amount of curvature is associated with the density of mass, energy, and momentum at the point.
In the beginning (in current big bang theology) all the stuff was close(er) together and the balloon was smaller so gravity was greater anywhere on the surface of the balloon and time was slower according to relativity.
More accurately, spacetime was more curved close to the BB. That curvature affects both space and time. But we can still set up a time coordinate that agrees with the 'proper time' experienced at each point.
One aspect of this is that time is relative: it isn't an absolute. Nor is distance. So, what I measure to be the time between two events may disagree with what you measure for the time between those events.
There are also 'paradoxes' like the twin paradox: if twins are both moving with respect to each other, each will see the clocks of the other as slowed. There is a symmetry here.
Seems to me the expansion of space drives time rather than the other way around. As time becomes faster and faster the distance light covers becomes less and less so light (photons) from far distance points become more and more delayed. If it is expansion of space that drives time wouldn't the age of the universe currently inferred by constant time and perhaps varying light speed be very wrong?
The distinction here is between a time coordinate, which only has to 'point' to the future, and the proper time of an observer. In a BB scenario, the time coordinate we choose is the proper time of comoving observers. To say time is 'faster and faster' misunderstands the spacetime geometry. Which, again, is consistent between observers, even if time duration (and distances) is not.
Just to humor me can anyone here comment as to how old the universe might be if time was considered a variable? I think scientists consider time constant from now back unto the beginning but if time in the beginning was a lot slower then time in the now then based on "now time" the universe could be infinitely older than predicted.
Part of the difficulty is what is meant by time being faster or slower. For a gravitational field, there is a difference in measured time between someone in the field and someone out of it. That is what is meant when we say time slows down. Having two viewpoints allows a comparison.
But for the universe as a whole, there is no outside observer with a clock. Time is part of the geometry of the universe (spacetime is, in fact, the geometry). So there are not two observers that can compare measured time durations.