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

TL;DR

The study develops a model-agnostic reconstruction of the late-time expansion using a node-based Gaussian-process interpolation for $E(z)=H(z)/H_0$, constrained by CC, Pantheon+, BAO, BAOtr, and $H_0$ priors. By mapping the reconstructed $H(z)$ onto an effective DE-fluid and then to scalar-field descriptions, it uncovers a robust indication of a sign change in the effective dark-energy density $ ho_{ m DE}$ at $z_ au$, with $ ho_{ m DE}<0$ at higher redshift and $ ho_{ m DE}>0$ today. A single-field canonical phantom framework cannot realize such a transition smoothly, whereas a two-field quintom model with a separable potential can accommodate smooth phantom-divide crossings via a sign-change in the net kinetic term $ abla Q^2- abla P^2$. The analysis also hints at an additional intermediate-redshift acceleration window around $z oughly 1.7$–$2.3$ in some data combinations, though the evidence is not decisive; Bayesian model comparison nevertheless favors ΛCDM given current data, underscoring the need for improved high-$z$ distance measurements and low-$z$ anchor precision to robustly test these features.

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 $ρ_{\rm DE}<0$ at higher redshift to $ρ_{\rm DE}>0$ toward the present, and defining a transition redshift $z_\dagger$ by $ρ_{\rm DE}(z_\dagger)=0$. 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 $ρ_{\rm DE}>0$ 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 $\sim1.5$--$1.7σ$ level.

Figures (22)

• Figure 1: Posterior predictive bands for the reconstructed kinematic quantities $H(z)$, $H(z)/(1+z)$, and $q(z)$ for three illustrative dataset combinations (top to bottom rows): CC+SN+DESI+H0DN, CC+MnM-BAOtr+H0DN, and CC+SN+H0DN. The color shading encodes the $\sigma$-equivalent credible level around the best-fit reconstruction, as indicated by the color bar in each panel (up to $\sim2.5\sigma$); for a Gaussian posterior, the $1\sigma$ and $2\sigma$ levels correspond approximately to 68% and 95% credible regions. The black dotted curve shows the best-fit reconstruction, while the green dotted curve shows the best-fit flat $\Lambda$CDM baseline for the same dataset combination. Since the highest-redshift node is at $z=3$ and there are no data in $2.4<z<3.0$, behavior in this interval should be interpreted cautiously, especially for derivative-based quantities.
• Figure 2: Posterior predictive bands for the effective dark-energy density $\rho_{\rm DE}(z)$, pressure $p_{\rm DE}(z)$ (both shown normalized to the present-day critical density as in the axis labels), and the equation of state $w_{\rm DE}(z)=p_{\rm DE}/\rho_{\rm DE}$ for the same three dataset combinations as in Fig. \ref{['fig:H_and_q']} (top to bottom rows): CC+SN+DESI+H0DN, CC+MnM-BAOtr+H0DN, and CC+SN+H0DN. The color shading encodes the $\sigma$-equivalent credible level around the best-fit reconstruction, as indicated by the color bar in each panel (up to $\sim2.5\sigma$). The black dotted curve shows the best-fit reconstruction, while the green dotted curve shows the best-fit flat $\Lambda$CDM baseline for the same dataset combination. The divergence of $w_{\rm DE}$ occurs when $\rho_{\rm DE}$ crosses zero and reflects the kinematic ratio $p_{\rm DE}/\rho_{\rm DE}$ rather than a singularity in $H(z)$. Since there are no data in $2.4<z<3.0$, behavior in this interval should be interpreted cautiously.
• Figure 3: Posterior predictive bands for the effective kinetic contribution $\Delta\mathcal{X}(z)$ and the total effective potential (denoted $V(z)$ in the plot), inferred from the reconstructed background for the same three dataset combinations as in Fig. \ref{['fig:H_and_q']} (top to bottom rows): CC+SN+DESI+H0DN, CC+MnM-BAOtr+H0DN, and CC+SN+H0DN. The color shading encodes the $\sigma$-equivalent credible level around the best-fit reconstruction, as indicated by the color bar in each panel (up to $\sim2.5\sigma$). The black dotted curve shows the best-fit reconstruction, while the green dotted curve shows the best-fit flat $\Lambda$CDM baseline for the same dataset combination. A change in the sign of $\Delta\mathcal{X}$ is naturally interpreted within the two-field (quintom) framework, in which the net kinetic contribution can change sign. Since there are no data in $2.4<z<3.0$, behavior in this interval should be interpreted cautiously.
• Figure 4: Two-dimensional marginalized posterior distributions for the derived transition redshift $z_\dagger$ versus $H_0$ (shown here for H0DN; SH0ES cases are nearly indistinguishable in our pipeline). Contours denote the 68% and 95% credible regions. The top row shows combinations without SN (as labeled in the panels), and the bottom row shows the corresponding combinations including SN. Combinations without SN exhibit a pronounced anticorrelation between $z_\dagger$ and $H_0$ in several cases, while adding SN significantly reduces this degeneracy and compresses the $H_0$ posterior toward $\sim70~{\rm km\,s^{-1}\,Mpc^{-1}}$.
• Figure 5: Two-dimensional marginalized posterior distribution for $z_\dagger$ versus $H_0$ illustrating the sensitivity of the inferred transition epoch to the assumed $\Omega_{m0}$ (shown here for the same dataset combination and $H_0$ prior as used in the underlying run). Lower $\Omega_{m0}$ shifts the inferred transition to higher $z_\dagger$, and vice versa.