An optimal basis system for cosmology: data analysis and new parametrization

We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimized for a specific cosmological model or for an ensemble of models, even if based on drastically different physical assumptions. The projection coefficients derived from this basis system, the so-called features, provide a common parametrization to study and compare different cosmological models independently of their physical construction. They can be used to directly compare different cosmologies and study their degeneracies in terms of a simple metric separation. This is a very convenient approach, since only a very small number of realizations have to be computed in contrast to Markov Chain Monte Carlo methods. Finally, the proposed basis system can be applied to reconstruct the Hubble expansion rate from supernova luminosity distance data with the advantage of being sensitive to possible unexpected features in the data set. We test the method both on mock catalogues and on the SuperNova Legacy Survey data set.