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

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 $0\lesssim z\lesssim 2.5$, including a Ly$\alpha$-forest anchor at $z_{\mathrm{e}\mathrm{f}\mathrm{f}}=2.33$. In CMB-calibrated combinations, flat $\mathrm{\Lambda }$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$\times {10}^{-2}$,mag level. To sharpen likelihood-level interpretation, we provide two diagnostics: (i) an $r_d$-independent BAO-shape observable, $F_{\mathrm{A}\mathrm{P}}(z)\equiv D_{\mathrm{M}}(z)\mathrm{/}{D}_{\mathrm{H}}(z)$, constructed directly from published $(D_{\mathrm{M}}\mathrm{/}{r}_d,D_{\mathrm{H}}\mathrm{/}{r}_d)$ with covariance propagation; and (ii) a linear-response map from SN Hubble-diagram systematics $\delta \mu (z)$ 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 ${\rho }_{\mathrm{D}\mathrm{E}}(z)$ and map the resulting phenomenology to microphysical dark-energy and modified-gravity models subject to perturbation stability and gravitational-wave propagation constraints.