  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 first-year SNLS data.
In particular, we show that the method is capable of reproducing a hypothetical
expansion function containing a sudden transition.
