What do the cosmological supernova data really tell us?

Abstract

We try to reconstruct the scale factor a(t) of the universe from the SNe Ia data, i.e. the luminosity distance dL(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 dL(z) rather than a(t), since dL(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 zt ∼ 0.50 ± 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 dL(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 dL(z) data.