How is the universe exactly 13.7 billion years old, in absence of absolute time?

[mitrasoumya]

Distribution of mass across the universe is not even. Therefore, passage of time should vary according to gravity. Which means at places time will pass at a higher pace or a lower pace than in respect of other places. Then, how is the entire Universe exactly 13.7 billion years old?

 

[Dale]

First, 13.7 isn't an exact number. It is a best fit to a model which is only valid at scales where the universe is homogenous.

Second, the same thing can be said of a human whose head spends, on average, more time at a higher gravitational potential than their feet.

 

[ibysaiyan]

The universe isn't exactly 13.7 billions as said above , we get that under the crude assumption that the expansion has been fairly constant since the BB , which it has not ( if I recall correctly this value is calculated by simply finding out the inverse of the Hubble's time , whose value varies).

 

[PeterDonis]

Distribution of mass across the universe is not even. Therefore, passage of time should vary according to gravity. Which means at places time will pass at a higher pace or a lower pace than in respect of other places. Then, how is the entire Universe exactly 13.7 billion years old?

The 13.7 billion year number (which, as DaleSpam points out, is only approximate anyway) does not apply to "the entire Universe". It is an estimate of the proper time experienced by "comoving" observers (observers who see the universe as homogeneous and isotropic at all times) since the Big Bang. Observers who see non-homogeneous or non-isotropic matter distributions will have experienced a different amount of proper time since the Big Bang; in other words, the passage of time *does* "vary according to gravity".

 

[Bill_K]

Although 13.7 Gy is almost universally quoted, the current best value is 13.75. See Wikipedia if you don't believe me!

 

[Adam Lewis]

Reiterating PeterDonis' point, 13.7 billion years is the time since the singularity in the rest frame of a special class of "comoving" observers. Comoving observers use coordinates which "factor out" cosmological expansion so that galaxies participating in the expansion are always at the same distance. Other observers measure different times. However, since the CMB is at its minimum energy in the comoving frame, a body moving with respect to a comoving observer will tend to come to rest, in a similar way to how a body moving through the ocean will tend to come to rest with respect to the water.

 

[PeterDonis]

Comoving observers use coordinates which "factor out" cosmological expansion so that galaxies participating in the expansion are always at the same distance.

This is not correct, at least not with the usual interpretation of the term "distance" as "proper distance". The proper distance between comoving observers does increase as the universe expands. The comoving observers stay at constant *spatial coordinates* in the standard FRW chart, meaning that they stay at the same "coordinate distance" from each other, but that's not the same as staying at the same proper distance from each other. The proper distance involves the metric, not just the coordinates, and the metric changes with time.

However, since the CMB is at its minimum energy in the comoving frame, a body moving with respect to a comoving observer will tend to come to rest, in a similar way to how a body moving through the ocean will tend to come to rest with respect to the water.

This is true, but it's a *very* small effect. The radiation pressure of the CMBR has no observable effect on the motion of any of the objects we can see, and certainly most of those are not on "comoving" worldlines.