Comoving Coordinate System........
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Comoving Coordinate System
In a Comoving Coordinate System, the measuring scale expands along with the frame (expanding universe).
Here, the [dr2+r2θ2+r2sin2θdϕ2][dr2+r2θ2+r2sin2θdϕ2] is the Comoving Distance, and the ds2ds2 is the Proper distance.
The proper distance will correspond to the actual distance as measured of a distant galaxy from earth at the time of observation, a.k.a. instantaneous distance of objects.
This is because the distance travelled by a photon when it reaches the observer from a distant source will be the one received at t=t0t=t0 of the observer, which would mean that the instantaneous observed distance will be the proper distance, and one can predict future distances using the rate factor and the initial measured length as a reference.
The concept of Comoving and proper distance is important in measuring the actual value of the number density of galaxies in the given volume of the observed space. One must use the Comoving distance to calculate the density at the time of their formation when the observed photon was emitted. That can be obtained once the rate of expansion of the universe can be estimated.
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