Age of the universe and time dilation
Given our knowledge and the standard cosmological model, we estimate that the age of the universe is about 13.7 billion years old.
How much sense does it make to talk about the age of the universe as a whole?
We can observe time dilation so we know time passes differently for observers moving at different speeds (special relativistic time dilation) or located at different distances from centres of strong gravitational fields (as explained by general relativity). Is the estimated age of the universe a property of the universe or of us as its observers?
Would a different observer perceive the age of the universe to be different? Do different parts of the universe have different ages? Do the principles of special relativity even apply when thinking on a universal scale?
This question is really focused on the interaction of time dilation with estimates of the age of the universe, which is not part of the linked question or included in its answer.
@Omen indeed, I've seen the question you linked to (I even extracted a quote from the answer to it) but what I'm asking is something entirely different. I know how we estimate the age of the universe but I'm not sure how to interpret this value with respect to general and special relativity.
The answer is yes time dilation does affect how much time an observer experiences since the big bang until the present (cosmological) time.
However there is a certain set of special observers called comoving observers, these are the observers to which the Universe appears isotropic to. For example we can tell the Earth is moving at about 350 km/s relative to a nearby comoving observer by measuring the anistropy in the cosmic microwave background (in fact it causes a relatively large anistropy, the pictures of the CMB you see from WMAP, etc are with this anistropy factored out).
One special property of a comoving observer in the Universe is that they maximize the age of the Universe, i.e. no other observer can experience more time since the big bang than a comoving observer (in case you ask there is no observer that minimizes the time since the big bang). When we talk about the age of the Universe we are talking about the age of the Universe from the pov of a comoving observer.