Curvature vs Distances: testing the FLRW cosmology

Abstract

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 {\it et al} test known as $\Omega_K(z)$, whose value is constant in redshift for the standard cosmological model, but deviates elsewise. We find good agreement with the expected values of the standard cosmological model within the experimental errors. Finally, we provide forecasts, exploiting the Baryon Acoustic Oscillations measurements from the Euclid survey.