Reconstruction of the dark energy scalar field potential by Gaussian process

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$\%$.