Aims. While weak lensing cannot resolve cluster cores and strong lensing is almost insensitive to density profiles outside the scale radius, combinations of both effects promise to constrain density profiles of galaxy clusters well, and thus to allow testing of the CDM expectation on dark-matter halo density profiles. Methods. We develop an algorithm further that we had recently proposed for this purpose. It recovers a lensing potential optimally reproducing observations of both strong and weak-lensing effects by combining high resolution in cluster cores with the larger-scale information from weak lensing. The main extensions concern the accommodation of mild non-linearity in inner iterations, the progressive increase in resolution in outer iterations, and the introduction of a suitable regularisation term. The linearity of the method is essentially preserved. Results. We demonstrate the success of the algorithm with both idealised and realistic simulated data, showing that the simulated lensing mass distribution and its density profile are well reproduced. We then apply it to weak and strong lensing data of the cluster MS 2137 and obtain a parameter-free solution which is in good qualitative agreement with earlier parametric studies.

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.

We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised 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 parameterisation for studying and comparing 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 very few realisations 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.

Based on the largest homogeneously reduced set of Type Ia supernova luminosity data currently available -the Union2 sample -we reconstruct the expansion history of the Universe in a model-independent approach. Our method tests the geometry of the Universe directly without reverting to any assumptions made on its energy content and thus allows us to constrain dark energy models in a straightforward way. This is demonstrated by confronting the expansion history reconstructed from the supernova data to predictions of several dark energy models in the framework of the w cold dark matter (wCDM) paradigm. In addition, we test various non-standard cosmologies such as braneworlds, f (R) and kinematical models. This is mainly intended to demonstrate the power of the method. Although statistical rigour is not the aim of our current study, some extreme cosmologies clearly disagree with the reconstructed expansion history. We note that the applicability of the presented method is not restricted to testing cosmological models. It can be a valuable tool for pointing out systematic errors hidden in the supernova data and planning future Type Ia supernova cosmology campaigns.