According to the definition I have encountered for the concept of cosmological time, it is defined in the following way:
The cosmological principle states that, at each location in the universe, it is possible to define a hypothetical observer to whom the universe appears homogeneous and isotropic. These observers are called comoving observers, and the comoving coordinate system is the system for which the comoving observers are at rest.
The time measured by the comoving observers is called cosmological time, and as a reference we set it to zero at the time of the Big Bang.
But, according to special relativity, the time interval that an observer measures as the duration of a certain event depends on the velocity of the observer. So, why is cosmological time unique, that is, independent of the point in space where the comoving observer is located? Wouldn't this mean that, in an expanding universe, all comoving observers have the same physical velocity? Am I misunderstanding some concept here?