Non-parametric 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 non-parametric 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 a Neural Network Regression, to analyze the Hubble Diagram in a completely non-parametric, model-independent fashion. We first validate the method through simulated samples with the same redshift distribution as the real ones, and discuss the limitations related to the "inversion problem" for the distance-redshift relation. We then apply this new technique to the analysis of the Hubble diagram of Supernovae and quasars. We confirm that the data up to $z \sim 1-1.5$ are in agreement with a flat ${\Lambda}CDM$ model with ${\Omega}_M \sim 0.3$, while $\sim 5$-sigma deviations emerge at higher redshifts. A flat ${\Lambda}CDM$ model would still be compatible with the data with ${\Omega}_M > 0.4$. Allowing for a generic evolution of the dark energy component, we find solutions suggesting an increasing value of ${\Omega}_M$ with the redshift, as predicted by interacting dark sector models.