Nonparametric analysis of the Hubble diagram with neural networks

¹ Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy
e-mail: lorenzo.giambagli@unifi.it
² naXys – Namur Center for Complex Systems, University of Namur, Rue Grafé 2, 5000 Namur, Belgium
³ INFN and CSDC, Via Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy
⁴ INAF – Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy

Received: 24 February 2023
Accepted: 10 July 2023

Abstract

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 Λ cold dark matter model with Ω_M ∼ 0.3, while ∼5-sigma deviations emerge at higher redshifts. A flat Λ cold dark matter model would still be compatible with the data with Ω_M > 0.4. Allowing for a generic evolution of the dark energy component, we find solutions that suggest an increasing value of Ω_M with redshift, as predicted by interacting dark sector models.