We often read about the expansion of the universe in the first seconds, or milliseconds after the big bang. What frame of reference is used for these estimates of time? If the entire universe was compacted that small, then gravitational time dilation would be huge and a millisecond of time would equate to much longer in our earth bound time frame. What reference is used?
The argument goes as follows.
First we model the universe as isotropic and homogeneous on the largest scale (i.e. smooth and the same in all directions and locations). Next we define a global reference frame, it is the one in which the matter in the universe does not move. The field equation of general relativity then provides a differential equation relating time in this reference frame to the energy density of the matter. This is the time measure that is being referred to when people speak of 'so and so milliseconds after the Big Bang'.
To get a feeling for what this time means in physical terms, one must look at the physical processes going on. For example, you can think of the half-life of particles such as baryons (once they had been formed in large numbers). At earlier times it can be thought of as indicated by the frequencies of the de Broglie waves. I think even experts struggle to develop physical intuition about this; one learns to rely more and more on the equations themselves. But the mathematics of general relativity also provides a metric, which is basically a set of conversion factors between the comoving reference frame (time,distance) and the (time,distance) in an inertially moving frame at any given place. It so happens that the conversion factor for the time is 1 in this example!
I gues the same reference as of today's ignoring the time dilation it's how much space formation was taking up per second that is defined by the excitation of the caesium isotope. The possibility of the dilation to have been felt by an intelligent organism was no existent. The exited state of matter back then was in form of the pure fundamental forces that we know of today. Not even quarks existed. And the universe was completely homogeneous untill the moment preceding the inflation. Tiny ripples in the universe at this stage are believed to be the basis of large-scale structures that formed much later which gave rise to relativistic approach to the universe that we use now.