On the luminosity distance and the epoch of acceleration

Understand

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 $z_{acc} \sim 0.7$.

• 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 $\Delta\mu$ 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, {\em not} the deceleration predicted by $\Lambda$CDM and relatives.