Discriminating among cosmological models by data-driven methods

We explores the Pantheon+SH0ES dataset to identify patterns that can discriminate between different cosmological models. We focus on determining whether the behaviour of dark energy is consistent with the standard $\Lambda$CDM model or suggests novel cosmological features. The central goal is to evaluate the robustness of the $\Lambda$CDM model compared with other dark energy models, and to investigate whether there are deviations that might indicate new cosmological insights. The study takes into account a data-driven approach, using both traditional statistical methods and machine learning techniques. Initially, we evaluate six different dark energy models using traditional statistical methods like Markov Chain Monte Carlo (MCMC), Static and Dynamic Nested Sampling to infer the cosmological parameters. Subsequently, we adopt a machine learning approach, developing a regression model to compute the distance modulus of each supernova, expanding the feature set to 74 statistical features. Traditional statistical analysis confirms that the $\Lambda$CDM 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/Modified Chaplygin Gas) show significant improvement after feature selection. The study demonstrates the effectiveness of a data-driven approach to cosmological model evaluation. The $\Lambda$CDM model remains robust, while machine learning techniques, in particular feature selection, reveal potential improvements in alternative models which could be relevant for new observational campaigns like the recent DESI survey.