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

TL;DR

This paper introduces a new null test based on the Weyl potential and Noether's theorem, utilizing machine learning to assess the consistency of the $ ext{Lambda CDM}$ model with upcoming survey data, potentially revealing deviations or tensions.

Contribution

It presents a novel null test derived from Noether's theorem that uses measurements of the Weyl potential and employs machine learning for model consistency checks.

Findings

The null test can potentially rule out several cosmological models at around 4σ with future data.

Machine learning via Genetic Algorithms effectively reconstructs mock catalogs for the null test.

The approach helps identify tensions in cosmological data and tests the $ ext{Lambda CDM}$ model's validity.

Abstract

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.