A Homogeneous Universe is defined as a universe which is the same in all places. It is one of the defining concepts of the “Cosmological Principle”, proposed initially by Einstein. This states that there is no special place in the universe but that the cosmos is isotropic and homogenous at any particular time. That is the universe is the same in all places, homogeneous, and also the same in all directions, isotropic. Another way of looking at it is that a homogenous universe will have the same mean density. Although an isotropic universe need not be homogeneous, a homogeneous universe will be isotropic.
Although it is clear that, at a local level, the universe is not homogeneous, eg planets, stars, galaxies etc., on large scales the cosmological principle is assumed.
The cosmological principle fits into the Concordance model of the universe, the standard ΛCDM (lambda cold dark matter) model which has been very successful at modelling the development of the universe since the Planck era.
Homogeneity also leads to the assumption that the laws of physics are the same throughout the universe and at all times, down to the Planck era at least. This fact, that the laws of physics are the same everywhere, enables us to define the concept of “cosmic time”.
As we know from relativity clock time depends on the nature of the frame of reference that we are in, compared with an alternative frame. The speed of the clock ticks in different frames of reference will not be the same. A clock in motion relative to the observer, or in a different gravity situation, will not measure proper time, ie time in the observer’s frame of reference, our frame if we are the observer.
However, in a homogeneous system, where the conditions are the same, we can define cosmic time as the situation whereby a clock placed in many locations in the universe will keep the same time relative to each other. Thus we can remove the effects of Hubble Flow, ie the expansion of space-time, and enable us to calculate cosmic time back to the origins of the universe. It can be considered as an objective, non observer dependent, rate of the flowing of time.
Cosmic time can therefore be used to determine the time since the Big Bang in the standard model. Using cosmic time=0 at the present gives us a “look back time” to the big bang of approximately 13.8 Gyr.