Reconstruction of a dark energy model for the Dirac-Born-Infeld scalar field with the Hubble and DESI data via Gaussian process

In this study, we reconstruct the dark energy (DE) as a Dirac-Born-Infeld (DBI) scalar field from the Hubble dataset (32 CC + 26 BAO) and the DESI dataset using the Gaussian process (GP). As the GP is a non-parametric and model-independent way to reconstruct a function and its derivative using the data, our reconstruction of the DE equation of state, the DE density parameter, and the potential does not assume any particular model of cosmology. Using Monte Carlo realizations of the GP-reconstructed expansion history, we derive a posterior estimate of the Hubble constant, obtaining H 0 = 69.53 plus or minus 2.68 km s-1 Mpc-1. This method offers a fully model-independent estimate of H 0, relying only on data and GP priors, and provides an unbiased intermediate value useful for reassessing the Planck-SH0ES tension. Using the reconstructed profiles of the scalar potential as a function of the field phi, along with their associated uncertainties, we perform a chi-square curve fitting procedure to assess the viability of four different scalar field potentials, such as Exponential, Power-law, Free Field (quadratic), and Higgs-like potential. This allows us to identify which potential best fits the reconstructed data. We also employ MCMC analysis to place quantitative constraints on the model parameters associated with each potential. Furthermore, we do a chi squared analysis for all four potentials and comment on the goodness of the fit for each of them. Finally, we discuss possible generalizations of our model-independent framework and outline the phenomenological implications of our findings.