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 z2. 5, including a Lyα-forest anchor at z ₄₅₅=2. 33. In CMB-calibrated combinations, flat ΛCDM exhibits a mild parameter mismatch, while allowing evolving dark energy (e. g. \ CPL w₀--wₐ) can improve the fit; the preference is dataset-dependent and is particularly sensitive to redshift-dependent SN calibration/selection residuals at the few10^-2\, mag level. To sharpen likelihood-level interpretation, we provide two diagnostics: (i) an rd-independent BAO-shape observable, F ₀₏ (z) D ₌ (z) /D ₇ (z), constructed directly from published (D ₌/rd, \, D ₇/rd) with covariance propagation; and (ii) a linear-response map from SN Hubble-diagram systematics δμ (z) to induced biases in (w₀, wₐ), 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 ₃₄ (z) and map the resulting phenomenology to microphysical dark-energy and modified-gravity models subject to perturbation stability and gravitational-wave propagation constraints.