Hints of sign-changing scalar field energy density and a transient acceleration phase at $z\sim 2$ from model-agnostic reconstructions

Abstract

We present a data-driven reconstruction of the late-time expansion history and its implications for dark-energy dynamics. Modeling the reduced Hubble rate with a node-based Gaussian-process-kernel interpolant, we constrain the reconstruction using CC, Pantheon+ SNIa, BAO data from SDSS and DESI, transversal BAO data, and external $H_0$ priors (SH0ES and H0DN). Assuming GR at the background level, we map the reconstructed kinematics onto a dark-energy fluid and a scalar-field description, yielding the total potential and kinetic contributions that reproduce the inferred $H(z)$. To interpret the reconstruction, we consider both a minimal single-field model (canonical or phantom) and a two-field (quintom) system consisting of one canonical and one phantom scalar field (or families). Within the GR-based effective-fluid mapping, the inferred dark-energy density changes sign for all dataset combinations explored, transitioning from ${\rho }_{\mathrm{DE}}<0$ at higher redshift to ${\rho }_{\mathrm{DE}}>0$ toward the present, and defining a transition redshift $z_{†}$ by ${\rho }_{\mathrm{DE}}(z_{†})=0$. A single canonical scalar cannot realize such a smooth evolution during expansion, whereas a phantom field or a two-field quintom framework can accommodate the required behavior; in particular, the two-field system permits smooth phantom-divide crossings at finite ${\rho }_{\mathrm{DE}}>0$ and distinguishes them from the separate notion of a density zero crossing. The reconstructed kinematics admit intermediate-redshift structure in some combinations, including hints of an additional accelerated-expansion interval around $z\sim 1.7$--$2.3$. The present-day equation of state remains close to a cosmological constant: combinations including supernovae give $w_0\simeq -1$, while combinations without supernovae but with an external $H_0$ prior show only a mild preference for $w_0<-1$ at the $\sim 1.5$--$1.7\sigma$ level.

42 pages total (24 pages main text; remainder appendices), 32 figures (4 in main text, 28 in appendices), 2 tables