Reconstruction of the dark energy scalar field potential by Gaussian process

Abstract: Dark energy is believed to be responsible for the acceleration of the universe. In this paper, we reconstruct the dark energy scalar field potential $V(\phi)$ using the Hubble parameter $H(z)$ through Gaussian Process analysis. Our goal is to investigate dark energy using various $H(z)$ datasets and priors. We find that the selection of prior and the $H(z)$ dataset significantly affects the reconstructed $V(\phi)$. And we compare two models, Power Law and Free Field, to the reconstructed $V(\phi)$ by computing the reduced chi-square. The results suggest that the models are generally in agreement with the reconstructed potential within a $3\sigma$ confidence interval, except in the case of Observational $H(z)$ data (OHD) with the Planck 18 (P18) prior. Additionally, we simulate $H(z)$ data to measure the effect of increasing the number of data points on the accuracy of reconstructed $V(\phi)$. We find that doubling the number of $H(z)$ data points can improve the accuracy rate of reconstructed $V(\phi)$ by 5$\%$ to 30$\%$.