Model-Independent Reconstruction of Quintessence Potential and Kinetic Energy from DESI DR2 and Pantheon+ Supernovae

Abstract

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 plus 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 $z\sim 1$, marking the dark energy-matter equality epoch. Notably, while apparent negative kinetic energy values emerge at intermediate redshifts (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.

Figures (3)

• Figure 1: Reliability assessment of reconstruction using four GP kernels based on Pantheon+SH0ES data ($H_0=67.3$, $\Omega_{m0}=0.3$).
• Figure 2: Non-parametric reconstruction of comoving distance $D_M(z)$ and its derivatives from SN Ia and BAO data using four kernel functions. Top row: Planck 2018 prior. Bottom row: PantheonPlus+SH0ES prior. Solid lines represent mean reconstructions from different kernels, while shaded regions denote 1$\sigma$ and $2\sigma$ confidence regions.
• Figure 3: Comparison of $U(z)$ and $\tau(z)$ reconstructions using different kernel functions under two distinct priors. Top row: Results with the Planck 2018 prior. Bottom row: Results with the PantheonPlus+SH0ES prior.