Dark Energy After DESI DR2: Observational Status, Reconstructions, and Physical Models

TL;DR

DESI DR2 tightens constraints on late-time cosmic acceleration by combining SNe Ia, BAO, CMB calibration, and perturbation probes, revealing mild tensions in flat ΛCDM that can be alleviated by evolving w(z) in dataset-dependent ways. The authors introduce two likelihood-level diagnostics, F_AP(z) and a linear-response SN bias map, to separate genuine late-time expansion changes from early-time ruler shifts and to translate calibration systematics into concrete w_0,w_a biases. They map reconstructed w(z) and ρ_DE(z) to microphysical models, emphasizing perturbation stability, GW propagation constraints, and the need for perturbation-level closure tests (growth, lensing, and 3×2pt analyses). The work provides a reproducible model-comparison framework, discusses the role of early-time physics such as EDE, and outlines near-term discriminants (shape BAO, standard sirens, and joint growth-geometry probes) essential for distinguishing CPL-like evolution from alternative explanations. Overall, the paper offers practical, likelihood-faithful diagnostics and a clear model-space roadmap to assess whether DESI-era hints of evolving dark energy reflect new physics or calibration and early-Universe physics.

Abstract

We review late-time cosmic acceleration after DESI Data Release~2 (DR2), emphasizing the interplay between Type~Ia supernovae (SNe~Ia), anisotropic BAO, CMB calibration, and perturbation-sensitive probes (RSD and weak lensing). DESI DR2 delivers percent-level BAO distance ratios over $0\lesssim z\lesssim2.5$, including a Ly$α$-forest anchor at $z_{\rm eff}=2.33$. In CMB-calibrated combinations, flat $Λ$CDM exhibits a mild parameter mismatch, while allowing evolving dark energy (e.g.\ CPL $w_0$--$w_a$) can improve the fit; the preference is dataset-dependent and is particularly sensitive to redshift-dependent SN calibration/selection residuals at the few$\times10^{-2}$\,mag level. To sharpen likelihood-level interpretation, we provide two diagnostics: (i) an $r_d$-independent BAO-shape observable, $F_{\rm AP}(z)\equiv D_{\rm M}(z)/D_{\rm H}(z)$, constructed directly from published $(D_{\rm M}/r_d,\,D_{\rm H}/r_d)$ with covariance propagation; and (ii) a linear-response map from SN Hubble-diagram systematics $δμ(z)$ to induced biases in $(w_0,w_a)$, yielding an explicit calibration requirement for DESI-era claims of evolving $w(z)$. We synthesize parametric and non-parametric reconstructions of $w(z)$ and $ρ_{\rm DE}(z)$ and map the resulting phenomenology to microphysical dark-energy and modified-gravity models subject to perturbation stability and gravitational-wave propagation constraints.

Figures (3)

• Figure 1: Response of relative SN distance moduli $\Delta\mu(z)\equiv \mu(z)-\mu(z_{\rm ref})$ (with $z_{\rm ref}=0.1$) to CPL parameters $(w_0,w_a)$ around a flat $\Lambda$CDM fiducial. These derivatives enter the linear-response bias mapping in Eq. (\ref{['eq:sn_param_bias']}) and quantify the redshift dependence required for SN calibration/selection systematics to bias $(w_0,w_a)$. Markers indicate the redshifts used in Table \ref{['tab:sn_w0wa_sensitivity']}.
• Figure 2: $r_d$-independent anisotropic-BAO "shape" observable $F_{\rm AP}(z)\equiv D_{\rm M}(z)/D_{\rm H}(z)$. The DESI DR2 Ly$\alpha$ point at $z_{\rm eff}=2.33$ is computed directly from the published anisotropic ratios $(D_M/r_d,\,D_H/r_d)$ values (with covariance propagated as in Eq. (\ref{['eq:FAP_fracvar']}) and statistical+theory-systematic terms added in quadrature for the plotted error bar), giving $F_{\rm AP}(2.33)=4.518\pm0.095_{\rm stat}\pm0.019_{\rm sys}$ (Table \ref{['tab:FAPvector']}). The curve shows the flat $\Lambda$CDM prediction for a Planck-like $\Omega_m$ (background shape only; independent of $H_0$ and $r_d$).
• Figure 3: Conversion between likelihood-ratio improvements $\Delta\chi^2$ and Gaussian-equivalent significance $N_\sigma$ for nested models with $k=1$ and $k=2$ additional parameters, using the two-sided mapping $p = 1-F_{\chi^2_k}(\Delta\chi^2)$ and $N_\sigma=\Phi^{-1}(1-p/2)$. This avoids the common (incorrect) shorthand $N_\sigma\simeq\sqrt{\Delta\chi^2}$ when $k\neq 1$.