The Mattig relation yields the angular-diameter distance, d A , as a function of redshift z for a universe with Ω Λ = 0. q 0 is the present-day value of the deceleration parameter, which measures the deceleration of the expansion rate of the Universe; in the simplest models, q 0 < 0.5 corresponds to the case where the Universe will expand forever, q 0 > 0.5 to closed models which will ultimately stop expanding and contract, q 0 = 0.5 corresponds to the critical case – Universes which will just be able to expand to infinity without re-contracting.