Reconstruction of the Quintessence Dark Energy Potential from a Gaussian Process

This paper presents the reconstruction of the quintessence dark energy potential in a model- independent way. Reconstruction relies on a Gaussian process and on available expansion rate data. Specifically, 40-point values of H(z) are used, consisting of a 30-point sample deduced from a differential age method and an additional 10-point sample obtained from the radial BAO method. Results are obtained for two kernel functions and for three different values of H₀. This sheds light on the H₀ tension problem indicating that it is not just a numerical problem. The model-independent reconstruction of the potential can serve as a reference to constraint available models and construct new ones. Various possibilities, including V(ϕ) ~ e^-λϕ , are compared with the reconstructions here obtained, which is notably the first truly model-independent reconstruction of the quintessence dark energy potential. This allows the selection of new models that can be interesting for cosmology. The method can be extended to reconstruct the potential of related dark energy models, to be considered in future work.