Solution

ID: past-exam-of-the-astrophysics-course-of-the-university-of-oxford/2015/8/f/ii/solution

For a small radial comoving interval, . At ,
Thus
This uses the unbound cosmological radial separation between separate quasars, unlike the peculiar-velocity redshift dispersion of galaxies inside the bound group. Integrating the distance relation instead of linearizing gives a small correction for a specified direction and endpoint. The quoted characteristic spacing alone does not assert that the same nearest object lies both purely transverse and purely radial.

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