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 ΛCDM 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 ΛCDM. First, we derive a joint consistency test for the spatial curvature Ω k, 0 and the matter density Ω 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 ΛCDM 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 ∼ 4 σ tension on the transition redshift as determined by the H ( z ) and radial BAO data.