Discriminating between cosmological models using data-driven methods

¹ Dipartimento di Fisica “E. Pancini”, Università degli Studi di Napoli “Federico II”, Complesso Univ. Monte S. Angelo, Via Cinthia 9, I-80126 Napoli, Italy
² Scuola Superiore Meridionale, Largo S. Marcellino 10, I-80138 Napoli, Italy
³ Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Complesso Univ. Monte S. Angelo, Via Cinthia 9, I-80126 Napoli, Italy
⁴ INAF – Astronomical Observatory of Capodimonte, Via Moiariello 16, I-80131 Napoli, Italy

^⋆ Corresponding author; capozziello@na.infn.it

Received: 3 August 2024
Accepted: 15 February 2025

Abstract

Context. This study examines the Pantheon+SH0ES dataset using the standard Lambda cold dark matter (ΛCDM) model as a prior and applies machine learning to assess deviations. Rather than assuming discrepancies, we tested the models’ goodness of fit and explored whether the data allow alternative cosmological features.

Aims. The central goal is to evaluate the robustness of the ΛCDM model compared with other dark energy models, and to investigate whether there are deviations that might provide new cosmological insights. This study takes a data-driven approach, using traditional statistical methods and machine learning techniques.

Methods. Initially, we evaluated six dark energy models using traditional statistical methods such as Monte Carlo Markov chain (MCMC) and static or dynamic nested sampling to infer cosmological parameters. We then adopted a machine learning approach, developing a regression model to compute the distance modulus for each supernova and expanding the feature set to 74 statistical features. We used an ensemble of four models: multi-layer perceptron, k-nearest neighbours, random forest regressor, and gradient boosting. Cosmological parameters were estimated in four scenarios using MCMC and nested sampling, while feature selection techniques (random forest, Boruta, and the Shapley additive explanation) were applied in three.

Results. Traditional statistical analysis confirms that the ΛCDM model is robust, yielding expected parameter values. Other models show deviations, with the generalised and modified Chaplygin gas models performing poorly. In the machine learning analysis, feature selection techniques, particularly Boruta, significantly improve model performance. In particular, models initially considered weak (generalised or modified Chaplygin gas) show significant improvement after feature selection.

Conclusions. This study demonstrates the effectiveness of a data-driven approach to cosmological model evaluation. The ΛCDM model remains robust, while machine learning techniques, in particular feature selection, reveal potential improvements to alternative models that could be relevant for new observational campaigns, such as the recent Dark Energy Spectroscopic Instrument survey.