Nonparametric analysis of the Hubble diagram with neural networks

The recent extension of the Hubble diagram of supernovae and quasars to redshifts much higher than 1 prompted a revived interest in nonparametric approaches to test cosmological models and to measure the expansion rate of the Universe. In particular, it is of great interest to infer model-independent constraints on the possible evolution of the dark energy component. Here we present a new method, based on neural network regression, to analyze the Hubble diagram in a completely nonparametric, model-independent fashion. We first validated the method through simulated samples with the same redshift distribution as the real ones, and we discuss the limitations related to the inversion problem for the distance-redshift relation. We then applied this new technique to the analysis of the Hubble diagram of supernovae and quasars. We confirm that the data up to z 1- 1.5 are in agreement with a flat cold dark matter model with ΩM 0.3, while 5-sigma deviations emerge at higher redshifts. A flat cold dark matter model would still be compatible with the data with ΩM > 0.4. Allowing for a generic evolution of the dark energy component, we find solutions that suggest an increasing value of ΩM with redshift, as predicted by interacting dark sector models.