Probing $\Lambda$CDM through the Weyl potential and machine learning forecasts

For years, the cosmological constant $\Lambda$ and cold dark matter (CDM) model ($\Lambda\text{CDM}$) has stood as a cornerstone in modern cosmology and serves as the predominant theoretical framework for current and forthcoming surveys. However, the latest results shown by the Dark Energy Spectroscopic Instrument (DESI), along other cosmological data, show hints in favor of an evolving dark energy. Given the elusive nature of dark energy and the imperative to circumvent model bias, we introduce a novel null test, derived from Noether's theorem, that uses measurements of the Weyl potential (the sum of the spatial and temporal distortion) at different redshifts. In order to assess the consistency of the concordance model we quantify the precision of this null test through the reconstruction of mock catalogs based on $\Lambda\text{CDM}$ using forthcoming survey data, employing Genetic Algorithms, a machine learning technique. Our analysis indicates that with forthcoming LSST-like and DESI-like mock data our consistency test will be able to rule out several cosmological models at around 4$\sigma$ and help to check for tensions in the data.