What do the cosmological supernova data really tell us?

Not much by themselves, aparently. We try to reconstruct the scale factor $a(t)$ of the universe from the SNe Ia data, i.e. the luminosity distance $d_{L}(z)$, using only the cosmological principle and the assumption that gravitation is governed by a metric theory. In our hence "model-independent," or "cosmographic" study, we fit functions to $d_{L}(z)$ rather than $a(t)$, since $d_{L}(z)$ is what is measured. We find that the acceleration history of the universe cannot be reliably determined in this approach due to the irregularity and parametrization-dependence of the results. However, adding the GRB data to the dataset cures most of the irregularities, at the cost of compromising the model-independent nature of the study slightly. Then we can determine the redshift of transition to cosmic acceleration as $z_{\rm t} \sim 0.50 \pm 0.09$ for a flat universe (larger for positive spatial curvature). If Einstein gravity (GR) is assumed, we find a redshift at which the density of the universe predicted from the $d_{L}(z)$ data is independent of curvature. We use this point to derive an upper limit on matter density, hence a lower limit on the density of dark energy. While these limits do not improve the generally accepted ones, they are derived *only using the $d_{L}(z)$ data*.