From Hubble diagrams to scale factors
  We present a lower bound on the radius of the universe today $a_0$ and a monotonicity constraint on the Hubble diagram. Our theoretical input is Einstein's kinematics and maximally symmetric universes. Present supernova data yield $a_0 > 1.2\cdot 10^{26}$ m. A first attempt to quantify the monotonicity constraint is described. We do not see any indication of non-monotonicity. 
Thomas Schucker, Andre Tilquin