Non-parametric analysis of the Hubble Diagram with Neural Networks

TL;DR

This paper introduces a neural network-based non-parametric method to analyze the Hubble Diagram, enabling model-independent constraints on dark energy evolution and revealing deviations at high redshifts.

Contribution

The authors develop and validate a neural network regression technique for non-parametric analysis of cosmological data, addressing limitations of traditional methods.

Findings

Data up to z~1-1.5 agree with flat ΛCDM model with Ω_M~0.3

Significant deviations (~5 sigma) appear at higher redshifts

Results suggest possible evolution of dark energy and increasing Ω_M with redshift

Abstract

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.