Cosmographic Hubble fits to the supernova data

Abstract

The Hubble relation between distance and redshift is a purely cosmographic relation that depends only on the symmetries of a Friedmann-Lemaitre-Robertson-Walker 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 interrelated cosmographic fits to the $\mathtt{l}\mathtt{e}\mathtt{g}\mathtt{a}\mathtt{c}\mathtt{y}\mathtt{05}$ and $\mathtt{g}\mathtt{o}\mathtt{l}\mathtt{d}\mathtt{06}$ supernova data sets. 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 ${\ensuremath{\chi}}^{2}$ fit to the luminosity distance, proper motion distance, angular diameter 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 parametrization $y=z/(1+z)$. 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.