Model-independent reconstruction of quintessence potential and kinetic energy from DESI DR2 and Pantheon+ Supernovae

We present a model-independent reconstruction of the quintessence scalar field’s dynamics—both its potential and kinetic energy—directly from the latest cosmological observations. Our analysis combines DESI DR2 baryon acoustic oscillation measurements with the Pantheon+ Type Ia supernova compilation, employing Gaussian process with four distinct covariance kernels to avoid theoretical priors on the potential’s functional form. Key findings reveal a monotonically decreasing potential with redshift, consistent with thawing quintessence, and a kinetic energy that crosses zero near z ~ 1 z ∼ 1 , marking the dark energy–matter equality epoch. Notably, while apparent negative kinetic energy values emerge at intermediate redshifts ( $$0.5<z<1.0$$ 0.5 < z < 1.0 ), these are statistical artifacts within uncertainties, arising from error amplification in derivative reconstruction rather than new physics. Our results demonstrate the power of non-parametric methods to constrain dynamical dark energy and show minimal dependence on the choice of cosmological priors, whether from local (SH0ES) or early-universe (Planck) measurements.