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
$S_8=\sigma_8\left(\Omega_m/0.3\right)^{0.5}$.
