Cosmographic Hubble fits to the supernova data

TL;DR

This paper performs cosmographic fits to supernova data to estimate the universe's acceleration without relying on dynamical models, highlighting uncertainties and the importance of parameterization choices.

Contribution

It introduces transparent graphical methods for analyzing redshift-distance relations and critically examines how different fitting choices affect the estimated deceleration parameter.

Findings

Evidence suggests an accelerating universe but not beyond reasonable doubt.

Fitted deceleration parameters vary significantly with distance measures and parameterizations.

Systematic uncertainties in supernova data impact the significance of acceleration conclusions.

Abstract

The Hubble relation between distance and redshift is a purely cosmographic relation that depends only on the symmetries of a FLRW spacetime, but does not intrinsically make any dynamical assumptions. This suggests that it should be possible to estimate the parameters defining the Hubble relation without making any dynamical assumptions. To test this idea, we perform a number of inter-related cosmographic fits to the legacy05 and gold06 supernova datasets. Based on this supernova data, the "preponderance of evidence" certainly suggests an accelerating universe. However we would argue that (unless one uses additional dynamical and observational information) this conclusion is not currently supported "beyond reasonable doubt". As part of the analysis we develop two particularly transparent graphical representations of the redshift-distance relation -- representations in which acceleration versus deceleration reduces to the question of whether the relevant graph slopes up or down. Turning to the details of the cosmographic fits, three issues in particular concern us: First, the fitted value for the deceleration parameter changes significantly depending on whether one performs a chi^2 fit to the luminosity distance, proper motion distance or other suitable distance surrogate. Second, the fitted value for the deceleration parameter changes significantly depending on whether one uses the traditional redshift variable z, or what we shall argue is on theoretical grounds an improved parameterization y=z/(1+z). Third, the published estimates for systematic uncertainties are sufficiently large that they certainly impact on, and to a large extent undermine, the usual purely statistical tests of significance. We conclude that the supernova data should be treated with some caution.