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

In general relativity (GR) on a Friedmann–Lemaˆıtre–Robertson–Walker (FLRW) background, late-time cosmic acceleration requires an effective component with equation of state w(z) ≡p/ρ<−1/3. The minimal description is a cosmological constant, w =−1 and ρΛ = ΩDEρcrit,0 with ρcrit,0 = 3H20 /(8πG), whose vacuum-energy interpretation faces radiative-instability and naturalness problems. We review the observational status of dark energy after the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2), emphasizing the interplay between Type Ia supernovae (SNe Ia), baryon acoustic oscillations (BAO), the cosmic microwave background (CMB), and perturbation-sensitive probes (redshift-space distortions and weak lensing). DESI DR2 provides percent-level BAO distance ratios over 0 ≲ z≲ 2.5 and a high-redshift Lyα-forest anchor at zeff = 2.33. In combinations with CMB data, flat ΛCDM exhibits a mild parameter discrepancy, while allowing the Chevallier–Polarski–Linder (CPL) w0–wa form (i.e. w0waCDM) can improve the fit; the reported preference is dataset-dependent and is sensitive to SN calibration and selection systematics at the few×10−2 mag level. To sharpen physical interpretation at the likelihood level, we provide two diagnostics: (i) an rd-independent anisotropic-BAO quantity, the Alcock–Paczynski parameter FAP(z) ≡DM(z)/DH(z), computed directly from the published (DM/rd, DH/rd) values; and (ii) a linear-response mapping that converts redshift-dependent SN distance-modulus systematics δµ(z) into characteristic biases in (w0,wa), thereby stating an explicit calibration requirement for DESI-era claims of evolving w(z). We synthesize reconstruction methods for w(z) and ρDE(z), and map phenomenology to microphysical models (scalar-field dark energy, interacting dark sectors, early-time physics that shifts rd, and modified gravity), including perturbation stability and gravitational-wave propagation constraints.