It is not. What you have there is an expression for the comoving distance.Apashanka said:For calculating the proper distance in cosmology why is the proper time between two points (galaxy) dΓ is taken 0??
e.g dΓ2=dt2-a(t)2dr2
Taking dΓ=0 and ∫dr=∫dt/a(t)
Comoving distance in cosmology is a measure of the distance between two objects in the universe, taking into account the expansion of the universe. It is the distance that two objects would be from each other if they were stationary and not affected by the expansion of the universe.
Comoving distance is different from proper distance because it takes into account the expansion of the universe, while proper distance does not. Proper distance is the physical distance between two objects at a specific point in time, while comoving distance is the distance between two objects at any given time, accounting for the expansion of the universe.
Comoving distance is calculated using the Hubble parameter, which describes the rate of expansion of the universe. It is also dependent on the cosmological model being used, as different models have different rates of expansion. It can be calculated using mathematical equations and is typically measured in units of megaparsecs (Mpc).
Comoving distance is significant in cosmology because it allows us to accurately measure distances between objects in the expanding universe. It also helps us understand the evolution of the universe and how objects have moved relative to each other over time. It is a crucial factor in determining the age and size of the universe.
Comoving distance and redshift are closely related in cosmology. Redshift is a measure of how much the light from an object has been stretched due to the expansion of the universe. The higher the redshift, the further away the object is and the larger the comoving distance. This relationship is described by Hubble's law, which states that the recessional velocity of an object is proportional to its distance from us.