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

TL;DR

This paper introduces a model-independent method to determine the universe's expansion rate using supernova data, avoiding assumptions about dark energy dynamics, and demonstrates its effectiveness on synthetic and real data.

Contribution

The paper presents a novel integral equation approach to recover the cosmic expansion rate without relying on specific cosmological models.

Findings

Method accurately reconstructs expansion history from synthetic data.

Successfully applied to real SNLS supernova data.

Capable of detecting sudden transitions in expansion rate.

Abstract

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.