Age of the universe and time dilation

Question

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?

Answer 1

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.

Answer 2

In the standard model, the universe looks the same for all locations moving in the local rest frame. This includes its apparent age. You can tell if you are in the local rest frame if the expansion of galaxies around you is symmetric in all directions and the microwave background also is the same in all directions. Simply put, any civilization on any galaxy in the visible universe would measure the same age of the universe that we do.

If, however, some object managed to move at nearly the speed of light relative to its local rest frames, which would have been changing continuously, for a significant fraction of the age of the universe, there would be relativistic time dilation and that object would not have aged as much as the rest of the universe. That is, if there were a clock onboard, it would record less time elapsed. However, since doing this requires continuous accelerations and vast energy, no natural phenomenon that we know of could have experienced this.

If an object accelerates to the speed of light and then cuts off its engines, then because of Hubble expansion, it will travel to locations where relative to the new local galaxies it is no longer going near the speed of light and hence the time dilation as seen by local observers drops off. Cosmologists usually use expanding coordinates, which expand in time with the global scale, to do calculations. In expanding coordinates this effect appears as a fictitious force (arising from the transformation of coordinate system) that acts to dampen velocities.