Does the age of the universe differ for observers in expanding space?

The age of the universe is said to be about 13.8 billion years. But, since time depends on the observer, would it be the same for a possible inhabitant of a planet in a galaxy about 10,000 million light years away that is separating from us at 60% of the speed of light?

mister i said:

The age of the universe is said to be about 13.8 billion years.

More precisely, the age of the universe according to comoving observers, i.e., observers who always see the universe as homogeneous and isotropic, is about 13.8 billion years.

mister i said:

would it be the same for a possible inhabitant of a planet in a galaxy about 10,000 million light years away that is separating from us at 60% of the speed of light?

If both galaxies are comoving (which galaxies are on average), yes. The "separation speed" you refer to has nothing to do with the "rate of time flow"; it is a coordinate speed and has no direct physical meaning.

What can affect the "rate of time flow", although in practice the effect is small, is the fact that particular observers might not be comoving. For example, we here on the Earth are not comoving; we observe a dipole anisotropy in the CMBR that tells us that, relative to a hypothetical comoving observer co-located with Earth, we are moving at about 600 km/s. That means our "rate of time flow" is not the same as that of a comoving observer. However, 600 km/s is still very small compared to the speed of light (about 0.2%), and the difference in the "age of the universe" for us on Earth as compared to a comoving observer is proportional to the square of that, or about 4 parts per million, which is way smaller than the measurement error in the 13.8 billion year figure. So 13.8 billion years still works just fine as our best estimate of the age of the universe according to us here on Earth.

A feature of our cosmological models is that they are the same everywhere. So if we say the universe is a certain age, so must observers in any other galaxy. This is one area where "neither galaxy is moving, but the space between them is expanding" is the simplest description.

Ibix said:

"neither galaxy is moving, but the space between them is expanding" is the simplest description.

And what happens regarding the light (which is indeed moving), from our point of observation it travels in this expanding space at 300,000 km/s or do we have to add the part of the spatial expansion?

mister i said:

And what happens regarding the light (which is indeed moving), from our point of observation it travels in this expanding space at 300,000 km/s or do we have to add the part of the spatial expansion?

One can think, by analogy, of an ant crawling down the length of an expanding rubber band.

mister i said:

And what happens regarding the light (which is indeed moving), from our point of observation it travels in this expanding space at 300,000 km/s or do we have to add the part of the spatial expansion?

Locally, you will always measure it to be doing ##c##. In the "expanding space" interpretation, the distance light still has to go to reach us is decreasing at less than ##c## because the space between us and it is expanding. Sufficiently distant light will never reach us because the total remaining distance is increasing faster than even light can decrease the distance.