The cosmological proper distance is given by

where a is the expansion parameter, r is the radius of the region in question, and c is the speed of light. From the Robertson-Walker line element,




where
is the curvature of the universe.

(1)
where a is the expansion parameter, r is the radius of the region in question, and c is the speed of light. From the Robertson-Walker line element,

(2)



(3)
where

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