: We all know that mass slows down the rate of time, right? So, given this, did time pass slower at the beginnings of the universe, : since all matter was clumped closer together? If so, does that have ramifications for our estimates of the age of the universe?

: I also wonder how much mass it takes to have an effect on time. Does a single atom slow time down?

The Friedmann-Robertson-Walker equation can be written ds2 = dct2 - R2(t)[dr2/(1 - kr2) + r2(dq2 + sin2qdf2)]

This gives the geometry for space-time in the case that it is homogenous and isotropic, and to a good extent it is, and it has been so as far back as we understand. There is a kind of time dilation that takes place, but it isn't directly related to the kind that you're thinking of. The coefficient in front of the time term dct is 1. If it were a function of time instead then it would have the kind of dilation you are thinking of. The reason it does not lies in the uniformity of the space. You chose a uniform density , not a sphere of mass of finite radius, but a uniform density extended throughout the space. If you want to find the age of the universe according to this space-time geometry you define that age in the following manner. Since the space is uniform, you can take anyplace to be the origin of the coordinates it uses. You might as well use here in the milky way as the origin. As you know the universe is expanding. Take a remote galaxy moving at a typical speed for that distance r. then find r as a function of time. The age of the universe can then be defined by the time at which the term (1 - kr2) equals zero resulting in a singularity in the above equation.

I don't think of it as the mass of an atom or anything slowing time down. I think of it as momentum and energy contributing(through differential equations) to kind of geometry that the space-time can have.