Curvature versus distances: Testing the FLRW cosmology

We test the FLRW cosmology by reconstructing in a model-independent way both the Hubble parameter $H(z)$ and the comoving distance $D(z)$ via the most recent Hubble and Supernovae Ia data. In particular we use data binning with direct error propagation, the principal component analysis, the genetic algorithms and the Pad\'e approximation. Using our reconstructions we evaluate the Clarkson et al. test known as ΩK(z), whose value is constant in redshift for the standard cosmological model, but deviates otherwise. Using present data, we find good agreement with the expected values of the standard cosmological model within the experimental errors, which are, however, large enough to allow for alternative cosmologies. A discrimination between the models may be possible for more precise future data. Finally, we provide forecasts, exploiting the baryon acoustic oscillation measurements from the Euclid survey.