On the luminosity distance and the epoch of acceleration

Abstract

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. 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 {\em amount} of acceleration since $z\sim 0.7$, but are weak at constraining $z_{acc}$; while radial BAO measurements are probably superior for placing direct constraints on $z_{acc}$.

arXiv commentLatex, 13 pages, 7 figures. Accepted by MNRAS. For the busy reader, Figs 4 and 6 are the main results

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• What do the cosmological supernova data really tell us?
• The effects of peculiar velocities in SN Ia environments on the local $H_0$ measurement
• Analysis of Pantheon+ supernova data suggests evidence of sign-changing pressure of the cosmological fluid