From Hubble diagrams to scale factors

Abstract

Context: .
Aims: .We study the image of the transform from scale parameters to Hubble diagrams and present a lower bound on the radius of the universe today a₀ and a monotonicity constraint on the Hubble diagram.
Methods: .Our theoretical input is minimal: Einstein's kinematics and maximally symmetric universes.
Results: .Present supernova data yield a₀ > 1.2× 10²⁶, i.e. Ω_k0 > -1.29. We attempt to quantify the monotonicity constraint and do not see any indication of non-monotonicity.
Conclusions: .