Evolution of dark energy reconstructed from the latest observations

TL;DR

This study directly reconstructs the effective dark energy density $X(z)$ in a largely model-independent, nonparametric Bayesian framework to explore DE dynamics beyond ΛCDM. Using a correlated prior and 40 scale-factor bins, they combine Planck, SNe, BAO, Ly$\alpha$FBAO, $H_0$, and OHD data to reveal oscillatory features around ΛCDM, including possible negative DE density at high redshift, with a best-fit model reducing χ^2 by 3.7σ but lacking robust Bayesian support under a standard prior. An evidence-weighted reconstruction suggests dynamical DE at about $2.5\sigma$, indicating genuine dynamical signatures under certain priors. The work cautions against EOS-based parameterizations in the presence of modified gravity and highlights the potential of upcoming surveys (DESI, Euclid, PFS) and gravitational-wave standard sirens to further test DE evolution.

Abstract

We reconstruct evolution of the dark energy (DE) density using a nonparametric Bayesian approach from a combination of latest observational data. We caution against parameterizing DE in terms of its equation of state as it can be singular in modified gravity models, and using it introduces a bias preventing negative effective DE densities. We find a $3.7σ$ preference for an evolving effective DE density with interesting features. For example, it oscillates around the $Λ$CDM prediction at $z\lesssim0.7$, and could be negative at $z\gtrsim2.3$; dark energy can be pressure-less at multiple redshifts, and a short period of cosmic deceleration is allowed at $0.1 \lesssim z\lesssim 0.2$. We perform the reconstruction for several choices of the prior, as well as a evidence-weighted reconstruction. We find that some of the dynamical features, such as the oscillatory behaviour of the DE density, are supported by the Bayesian evidence, which is a first detection of a dynamical DE with a positive Bayesian evidence. The evidence-weighted reconstruction prefers a dynamical DE at a $(2.5\pm0.06)σ$ significance level.

Figures (6)

• Figure 1: Panel (A): $X(z)$ (best-fit and 68% CL uncertainty) reconstructed using our standard correlated prior (blue filled band) compared to $X(z)$ derived from $w^{\rm eff}_{\rm DE}(z)$ reconstructed in Zhao:2017cud (black curves and a data point with error bars); Panel (B): the reconstructed effective DE pressure $Y(z)\equiv P^{\rm eff}_{\rm DE}(z)/\rho^{\rm eff}_{\rm DE}(0)$; Panel (C): the reconstructed deceleration parameter $q(z)$. For reconstructions in panels (A-C), the range of variation of $X$ in each bin is set by $\Delta_X=4$. Panels (D-F): the same quantities as in panels (A-C) but reconstructed using $\Delta_X=0.09$ (black solid curves), and the evidence-weighted reconstruction defined in Eq. (\ref{['eq:weighted']}) (blue filled band). The wine dash-dotted curves in panels (C) and (F) show the best-fit $q(z)$ in $\Lambda$CDM, and the dashed horizontal lines show $q=0$ to guide the eye. The dashed horizontal lines in panels (A,B,D,E) correspond to the $\Lambda$CDM model.
• Figure 2: Top panel: $H(z)$ derived from the reconstructed $X(z)$ rescaled by that of the best fit $\Lambda$CDM model. The data points with error bars show the measurements of $H$ as illustrated in the legend; Lower panel: same as the top panel but for the angular diameter distance $D_A$.
• Figure 3: The Bayes factor relative to that of the $\Lambda$CDM ($\Delta \,\rm lnE$) and the significance level of deviation from $\Lambda$CDM ($\rm S/N \equiv \sqrt{|\Delta \chi^2|}$) for different values of $\Delta_X$ that set the range of variation of $X$ in each bin.
• Figure 4: The reconstructed evolution of $X(z) \equiv \rho^{\rm eff}_{\rm DE}(z)/\rho^{\rm eff}_{\rm DE}(0)$ (white line with the 1$\sigma$ blue band around it) obtained by fitting 40 bins uniformly spaced in $a\in[1,0.01]$ with the help of our standard prior ($a_c=0.06$, $\sigma_m=0.04$). The discrete error bars show the 1$\sigma$ uncertainties on the bins from the prior alone. This reconstruction is compared to two cases where the last 8 bins, in the $a\in[0.001,0.206]$ range ($3.85<z<1000$), are replaced with a single wide bin: one in which it is allowed to vary independently (red solid lines showing the best fit and the 1$\sigma$ band) and one where it is fixed to 1 (green dashed lines).
• Figure 5: Comparison of the $X(z)$-reconstructions obtained using different values of the correlated prior parameters $a_c$ and $\sigma_m$, and the range $\Delta_X$ over which $X$ can vary in each bin. The discrete error bars show the 1$\sigma$ uncertainties from the prior alone. Panel (C) is the case of our standard prior, also shown in Fig. \ref{['fig:comlastbin']}. Note that the vertical axis range in Panel (G) differs from that in other panels.