Dynamical Dark Energy in the Crosshairs: A Joint Analysis with DESI, Type Ia Supernovae, and TDCOSMO Constraints

Abstract In this work, we perform a comprehensive joint analysis of three representative dark energy models—ΛCDM, the Chevallier–Polarski–Linder (CPL) parameterization, and the Generalized Emergent Dark Energy (GEDE) model—using the latest observational data sets: baryon acoustic oscillation measurements from Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) and 2 (DR2), Type Ia supernovae, and time-delay cosmography from Time-Delay COSMOgraphy (TDCOSMO) lensing. The CPL model yields a statistically significant improvement over ΛCDM, with ΔAIC = −0.54 for DESI DR2+Dark Energy Survey Y5+TDCOSMO, favoring a quintessence-like behavior ( w 0 = − 0.8 2 − 0.05 + 0.05 , w a = − 0.4 3 − 0.31 + 0.32 at 1 σ confidence level). The GEDE model also exhibits slightly favoring than ΛCDM with observations, yielding ΔAIC = −2.15. The captured potential dark energy evolution transition parameter Δ in GEDE model is constrained to − 0.5 2 − 0.20 + 0.22 (DR1) and − 0.5 0 − 0.17 + 0.18 (DR2), showing a 2.4 σ and 2.9 σ deviation from zero, respectively. This more than 2 σ statistically significant of nonzero value of Δ provides evidence against a pure cosmological constant scenario. The negative sign indicates quintessence-like behavior ( w > −1) in the late universe. Notably, the GEDE constraints show a more than 3 σ tension with the Δ = 1 (Phenomenological Emergent Dark Energy model) predictions. This significant discrepancy implies that while both models belong to the emergent dark energy family, their fundamentally different transition mechanisms lead to distinct cosmological implications. Our results collectively suggest that GEDE provides a phenomenologically viable alternative to ΛCDM.