Machine Learning and cosmographic reconstructions of quintessence and the Swampland conjectures

We present model independent reconstructions of quintessence and the Swampland conjectures (SC) using both Machine Learning (ML) and cosmography. In particular, we demonstrate how the synergies between theoretical analyses and ML can provide key insights on the nature of dark energy and modified gravity. Using the Hubble parameter $H(z)$ data from the cosmic chronometers we find that the ML and cosmography reconstructions of the SC are compatible with observations at low redshifts. Finally, including the growth rate data $f\sigma_8(z)$ we perform a model independent test of modified gravity cosmologies through two phase diagrams, namely $H-f\sigma_8$ and $\eta-f\sigma_8$, where the anisotropic stress parameter $\eta$ is obtained via the $E_g$ statistics, which is related to gravitational lensing data. While the first diagram is consistent within the errors with the $\Lambda$CDM model, the second one has a $\sim 2\sigma$ deviation of the anisotropic stress from unity at $z\sim 0.3$ and a $\sim 4\sigma$ deviation at $z\sim 0.9$, thus pointing toward mild deviations from General Relativity, which could be further tested with upcoming large-scale structure surveys.