Novel null tests for the spatial curvature and homogeneity of the
  Universe and their machine learning reconstructions
  A plethora of observational data obtained over the last couple of decades has
allowed cosmology to enter into a precision era and has led to the foundation
of the standard cosmological constant and cold dark matter paradigm, known as
the $\Lambda$CDM model. Given the many possible extensions of this concordance
model, we present here several novel consistency tests which could be used to
probe for deviations from $\Lambda$CDM. First, we derive a joint consistency
test for the spatial curvature $\Omega_{k,0}$ and the matter density
$\Omega_\textrm{m,0}$ parameters, constructed using only the Hubble rate
$H(z)$, which can be determined directly from observations. Second, we present
a new test of possible deviations from homogeneity using the combination of two
datasets, either the baryon acoustic oscillation (BAO) and $H(z)$ data or the
transversal and radial BAO data, while we also introduce two consistency tests
for $\Lambda$CDM which could be reconstructed via the transversal and radial
BAO data. We then reconstruct the aforementioned tests using the currently
available data in a model independent manner using a particular machine
learning approach, namely the Genetic Algorithms. Finally, we also report on a
$\sim 4\sigma$ tension on the transition redshift as determined by the $H(z)$
and radial BAO data.
