Friedmann-Lemaitre models...
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If pressure is negligible, the F-L Eqs. can be written as:



and



Now look at the propagation of light rays in a FRWL universe.  
Since

and from the RW metric:

Integrate over the light path:


This connects the comoving distance          with the
geometric distance         , evaluated from the integral:



From the FL eqs. in the reduced form:



and thus, substituting



where