On the luminosity distance and the epoch of acceleration.

Standard cosmological models based on general relativity (GR) with dark energy predict that the Universe underwent a transition from decelerating to accelerating expansion at a moderate redshift zacc ~ 0.7. Clearly, it is of great interest to directly measure this transition in a model-independent way, without the assumption that GR is the correct theory of gravity. We explore to what extent supernova (SN) luminosity distance measurements provide evidence for such a transition: we show that, contrary to intuition, the well-known 'turnover' in the SN distance residuals µ relative to an empty (Milne) model does not give firm evidence for such a transition within the redshift range spanned by SN data. The observed turnover in that diagram is predominantly due to the negative curvature in the Milne model, not the deceleration predicted by cold dark matter and relatives. We show that there are several advantages in plotting distance residuals against a flat, non-accelerating model (w = -1/3), and also remapping the z-axis to u = ln(1 + z); we outline a number of useful and intuitive properties of this presentation. We conclude that there are significant complementarities between SNe and baryon acoustic oscillations (BAOs): SNe offer high precision at low redshifts and give good constraints on the net amount of acceleration since z ~ 0.7, but are weak at constraining zacc; while radial BAO measurements are probably superior for placing direct constraints on zacc. [ABSTRACT FROM AUTHOR]