(c) [2.Opt]: The physical luminosity distance is related to the comoving proper distance in a flat Universe via equality d = (1 + z )D. Show that 2 D(1 + 3w) 3(1 + w) dL = D 1- 3cto(1 + w) in a flat universe dominated by a fluid with an equation of state w > - 1/3. So, what would be its flux received by us today if the comoving proper 3cto (1 + w) distance between Earth and the galaxy is D - no matter (1 + 3w) how luminous it is