Gaussian process reconstruction of scalar field dynamics from recent cosmological data

Abstract

We reconstruct the late-time expansion history and dark energy dynamics using available cosmological data. We consider dark energy as an effective minimally coupled canonical scalar field without assuming a specific form for its potential. For reconstruction, we use Gaussian Process (GP) regression with a joint dataset consisting of 32 cosmic chronometer measurements (CC32), DESI DR2 baryon acoustic oscillation data, three Type Ia supernova compilations (Pantheon+, Union3, and DES Y5), and compressed CMB distance priors. From the reconstructed Hubble parameter and its derivatives, we obtain the scalar field kinetic and potential energy densities, the equation of state $w(z)$, and the dimensionless slope parameter $|\lambda (z)|$ of the scalar field potential. The reconstructed potential is nearly constant at late times, with $\tilde{V}(0)\simeq 0.68$--$0.70{\rho }_{c,0}$, close to the dark-energy density in flat $\Lambda$CDM. The kinetic term remains small over $0\lesssim z\lesssim 2.5$, while $w(z)$ remains close to $-1$ within the uncertainties. Using only CC32 and DESI DR2, we find a mild ($1\sigma$) hint of a phantom-divide crossing near $z\sim 0.5$. However, this feature depends on the supernova compilation and cannot be regarded as a firm conclusion with current data. The slope parameter $|\lambda (z)|$ shows mild evolution, with present-day central values around $0.8$--$1.0$, but large uncertainties due to its dependence on higher-order derivatives of the expansion history. The curvature parameter $\Gamma (z)$ requires even higher-order derivatives and is not constrained by current data; therefore, we do not report its reconstruction. Allowing small spatial curvature, ${\Omega }_k=0$--$0.02$, changes the results only slightly and remains within the existing uncertainty bands.