There is a closed-form expression for the integral in the definition of the comoving distance if Ω Ω r = Ω Ω m = 0 or, by substituting the scale factor a for 1 / ( 1 + z ) , if Ω Ω Λ Λ = 0 . Our universe now seems to be closely represented by Ω Ω r = Ω Ω k = 0. In this case, we have: d C ( z ) = d H Ω Ω m − − 1 / 3 Ω Ω Λ Λ − − 1 / 6 [ f ( ( 1 + z ) ( Ω Ω m / Ω Ω Λ Λ ) 1 / 3 ) − − f ( ( Ω Ω m / Ω Ω Λ Λ ) 1 / 3 ) ] where f ( x ) ≡ ≡ ∫ ∫ 0 x d x x 3 + 1