Reconstruction of the quintessence dark energy potential from a Gaussian process

TL;DR

This paper presents the first truly model-independent reconstruction of the quintessence dark energy potential using Gaussian processes and expansion-rate data, providing insights into the H0 tension and guiding future model development.

Contribution

It introduces a novel, model-independent method for reconstructing the quintessence potential, applicable to various dark energy models and addressing the H0 tension.

Findings

Reconstructed the potential using Gaussian processes with different kernels and H0 values.

Indicated the H0 tension is related to physical understanding, not just statistical issues.

Provided a reference for constraining and developing dark energy models.

Abstract

The quintessence dark energy potential is reconstructed 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 $H_{0}$. They shed light on the $H_{0}$ tension problem for a universe described with quintessence dark energy. They are also a clear indication that the tension has to do with the physical understanding of the issue, rather than being just a numerical problem with statistics. Moreover, the model-independent reconstruction of the potential here obtained can serve as a reference to constraint available models and it can be also used as a reference frame to construct new ones. Various possibilities, including $V(\phi) \sim e^{-\lambda \phi}$, are compared with the reconstructions here obtained, which is notably the first truly model independent reconstruction of the quintessence dark energy potential. This allows to select 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.