Reconstructing dark energy with model independent methods after DESI DR2 BAO

TL;DR

This work tests whether dark energy is dynamical by applying two model-independent reconstructions—redshift binning and polynomial interpolation—to DESI DR2 BAO data combined with CMB distance priors and SN compilations. It reconstructs both the dark-energy equation of state $w(z)$ and the normalized density $f(z)$ without prescribing a fixed functional form, using three bin counts ($n=3,4,5$) and three node-based interpolations ($n=3,4,5$). The analyses consistently indicate DE evolution with redshift, with $w(z)$ decreasing in $0.5<z<1.5$ and crossing $-1$ (quintom-like behavior), and $f(z)$ rising at low redshift then declining beyond $z>1$, while high-redshift constraints remain weak. Importantly, these conclusions are robust across reconstruction methods and SN datasets, underscoring potential departures from the cosmological constant and motivating richer high-z data to refine the picture.

Abstract

In this paper, we employ two model-independent approaches, including redshift binning method and polynomial interpolation method, to reconstruct dark energy (DE) equation of state (EoS) $w(z)$ and DE density function $f(z)$. Our analysis incorporates data from the Dark Energy Spectroscopic Instrument (DESI) data release 2, Cosmic Microwave Background (CMB) distance priors from Planck 2018 and Atacama Cosmology Telescope data release 6, and three Type Ia supernovae (SN) compilations (PantheonPlus, Union3, and DESY5). To ensure model independence, we adopt three redshift binning schemes (n=3, 4, 5) and three polynomial interpolation schemes with the same number of nodes (n=3, 4, 5). Our main conclusions are as follows: 1) After taking into account DESI data, there is a trend that DE should evolve with redshift (with deviations from the cosmological constant reaching at least a $2.13σ$ confidence level), indicating that current observations favor a dynamical DE. 2) In the redshift range $0.5 < z < 1.5$, the DE EoS w(z) exhibits a decreasing trend and crosses the phantom divide $w=-1$, suggesting quintom-like behavior. 3) The DE density f(z) first increases at low redshift, reaching a hump around $z\approx 0.5$, and then decreases at $0.5 < z < 1.5$, with a rapid decrease at $z>1.0$. 4) For $z > 1.5$, current data are insufficient to place strong constraints on the evolution of DE, resulting in large uncertainties in the DE reconstruction. It must be emphasized that, these four main conclusions are independent of specific reconstruction models, and are insensitive to the choice of SN compilations.

Figures (10)

• Figure 1: Lagrange polynomial interpolants built from $n=2,3,4,5$ nodes (n is the number of nodes, degree is $n-1$). Red crosses indicate the given nodes. The dashed lines correspond to the linear ($n=2$), quadratic ($n=3$), cubic ($n=4$), and quartic ($n=5$) interpolants. A higher polynomial degree requires more nodes.
• Figure 2: Reconstruction of the DE EoS $w(z)$ (upper panels) and the corresponding DE density $f(z)$ using three redshift bins. Red dashed lines denote the best-fit values within each bin, while the blue dashed lines correspond to the best-fit CPL model for comparison. Shaded regions represent the 68% (dark gray) and 95% (light gray) confidence intervals. Results presented from left to right columns combine DESI BAO + CMB data with PantheonPlus, Union3, and DESY5 supernovae datasets, respectively.
• Figure 3: Reconstruction of the DE EoS $w(z)$ (upper panels) and the corresponding DE density $f(z)$ using four redshift bins. Red dashed lines denote the best-fit values within each bin, while the blue dashed lines correspond to the best-fit CPL model for comparison. Shaded regions represent the 68% (dark gray) and 95% (light gray) confidence intervals. Results presented from left to right columns combine DESI BAO + CMB data with PantheonPlus, Union3, and DESY5 supernovae datasets, respectively.
• Figure 4: Reconstruction of the DE EoS $w(z)$ (upper panels) and the corresponding DE density $f(z)$ using five redshift bins. Red dashed lines denote the best-fit values within each bin, while the blue dashed lines correspond to the best-fit CPL model for comparison. Shaded regions represent the 68% (dark gray) and 95% (light gray) confidence intervals. Results presented from left to right columns combine DESI BAO + CMB data with PantheonPlus, Union3, and DESY5 supernovae datasets, respectively.
• Figure 5: Reconstruction of the DE density $f(z)$ using three, four, and five redshift bins (upper, middle, and lower rows, respectively). Red dashed lines denote the best-fit values within each bin, while the blue dashed lines correspond to the best-fit CPL model for comparison. Shaded regions represent the 68% (dark gray) and 95% (light gray) confidence intervals. Results presented from left to right columns combine DESI BAO + CMB data with PantheonPlus, Union3, and DESY5 supernovae datasets, respectively.