Improving data-driven model-independent reconstructions and updated constraints on dark energy models from Horndeski cosmology

In light of the statistical performance of cosmological observations, in this work we present an improvement on the Gaussian reconstruction of the Hubble parameter data $H(z)$ from Cosmic Chronometers, Supernovae Type Ia and Clustering Galaxies in a model-independent way in order to use them to study new constraints in the Horndeski theory of gravity. First, we have found that the prior used to calibrate the Pantheon supernovae data significantly affects the reconstructions, leading to a 13$sigma $ tension on the $H_0$ value. Second, according to the $chi^{2}$-statistics, the reconstruction carried out by the Pantheon data calibrated using the $H_{0} $ value measured by The Carnegie-Chicago Hubble Program is the reconstruction which fits best the observations of Cosmic Chronometers and Clustering of Galaxies datasets. Finally, we use our reconstructions of $H(z)$ to impose model-independent constraints in dark energy scenarios as Quintessence and K-essence from general cosmological viable Horndeski models, landscape in where we found that a Horndeski model of the K-essence type can reproduce the reconstructions of the late expansion of the universe within 2$sigma$.