Model-independent determination of the cosmic expansion rate. I. Application to type-Ia supernovae

Aims. In view of the substantial uncertainties regarding the possible dynamics of the dark energy, we aim at constraining the expansion rate of the universe without reference to a specific Friedmann model and its parameters. Methods. We show that cosmological observables integrating over the cosmic expansion rate can be converted into a Volterra integral equation which is known to have a unique solution in terms of a Neumann series. Expanding observables such as the luminosity distances to type-Ia supernovae into a series of orthonormal functions, the integral equation can be solved and the cosmic expansion rate recovered within the limits allowed by the accuracy of the data. Results. We demonstrate the performance of the method applying it to synthetic data sets of increasing complexity, and to the firstyear SNLS data. In particular, we show that the method is capable of reproducing a hypothetical expansion function containing a sudden transition.