Comoving distance in cosmology

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SUMMARY

The discussion centers on the calculation of proper distance in cosmology, specifically addressing why the proper time between two galaxies, denoted as dΓ, is taken to be zero. The equation dΓ² = dt² - a(t)²dr² is analyzed, leading to the conclusion that dΓ=0 simplifies the integration of comoving distance as ∫dr = ∫dt/a(t). This approach is crucial for deriving cosmological redshift by relating the comoving distance traveled by signals to the scale factor history.

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Apashanka
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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)
 
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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)
It is not. What you have there is an expression for the comoving distance.

In the particular case you are referring to, it is part of a derivation of cosmological redshift based on expressing the comoving distance traveled by two consecutive signals in terms of the scale factor history and using that to find the time difference at emission to be compared to the time difference at reception.
 

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