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Relativity tells us that there is no preferred reference frame, yet current cosmology does operate on the hypothesis that all points in the observable universe originate from the same big bang instanton. So in principle there is a common point to measure time from throughout the universe. It seems at a minimum every observer should be able to measure time relative to the recombination period made famous by the CMB "baby picture".

I'm curious why we would not be able to use that as a common clock start point? Or also any non-trivial discussion of this with respect to General Relativity

Additional Note: Ref 1 provides good introductory discussion of how CMB can be treated as a unique reference frame with respect to special relativity. I would acknowledge such a statement may be slightly discordant to some, but it is non-trivial. It is hard to escape that the universe has come equipped with an identifiable physical clock signal with definitive start time.

1. Inflation and the Cosmic Microwave Background

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Indeed, you can certainly choose to measure time from any physically identifiable event, whether that is some specific configuration of the planets in the solar system, some star going supernova, or the Big Bang. The Big Bang has the advantage that it happened everywhere in the universe, so you don’t have to worry about delays. The same observations that we use here to identify that time could be used elsewhere to do the same.

This in no way violates the principle that there is no preferred frame. While we can choose cosmological time for our time coordinates, the laws of physics do not change if we make a different choice. A preferred frame is not just one that we are able to construct, but one in which the laws of physics are different than in any other frame.

So, although we can use cosmological time, we do not have to change the laws of physics to do so. Therefore it does not constitute a preferred frame

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