Gaussian Processes Reconstruction of the Dark Energy Potential

Scalar Fields (SF) have emerged as natural candidates for dark energy as quintessential or phantom fields, as they are the main ingredient of inflation theories. Instead of assuming some form for the scalar field potential, however, this work reconstructs the SF potential directly from observational data, namely, \textbf{Hubble and SNe Ia data}. We show that two popular forms for the SF potentials, namely, the power-law and the quadratic free-field, are compatible with the reconstructions thus obtained, at least for some choices of the priors of the matter density and curvature parameters and for some redshift intervals.