Testing the $\Lambda$CDM paradigm with growth rate data and machine learning

The cosmological constant $\Lambda$ and cold dark matter (CDM) model ($\Lambda\text{CDM}$) is one of the pillars of modern cosmology and is widely used as the de facto theoretical model by current and forthcoming surveys. As the nature of dark energy is very elusive, in order to avoid the problem of model bias, here we present a novel null test at the perturbation level that uses the growth of matter perturbation data in order to assess the concordance model. We analyze how accurate this null test can be reconstructed by using data from forthcoming surveys creating mock catalogs based on $\Lambda\text{CDM}$ and three models that display a different evolution of the matter perturbations, namely a dark energy model with constant equation of state $w$ ($w$CDM), the Hu \& Sawicki and designer $f(R)$ models, and we reconstruct them with a machine learning technique known as the Genetic Algorithms. We show that with future LSST-like mock data our consistency test will be able to rule out these viable cosmological models at more than 5$\sigma$, help to check for tensions in the data and alleviate the existing tension of the amplitude of matter fluctuations $S_8=\sigma_8\left(\Omega_m/0.3\right)^{0.5}$.