Probing Generalized Emergent Dark Energy with DESI DR2

As an update on the initial findings of DESI, the new results provide the first hint of potential deviations from a cosmological constant ($\omega=-1$), which, if confirmed with significance $>(2-4)\sigma$, would challenge the validity of $\Lambda$ within the $\Lambda$CDM model. We explore the Generalized Emergent Dark Energy (GEDE) model using recent BAO measurements from DESI DR2, Type Ia supernova compilations, and CMB distance priors. Employing nested sampling, we constrain the parameter $\Delta$, which characterizes deviations from $\Lambda$CDM. Our analysis shows that with CMB+DESI DR2 alone, GEDE tends to prefer positive values of $\Delta$. However, when different SNe Ia calibrations are included, the model favors negative values of $\Delta$, corresponding to an earlier injection of dark energy. The Marginalized constraints on $\omega(z)$ further shows that GEDE sharply emerges but then asymptotes to $\omega=-1$ without crossing it. At $z \sim 1$ data, GEDE provides a better fit than $\Lambda$CDM, while at $z \lesssim 0.5$ the data favor $\omega > -1$, bringing the model deviate from $\Lambda$CDM. Bayesian model comparison shows weak support for GEDE with CMB+DESI DR2 ($\ln BF=1.96$), moderate with PP ($\ln BF=2.65$), weak-to-moderate with Union3 ($\ln BF=2.34$), and weak with DES-SN5Y ($\ln BF=1.44$). Overall, GEDE is consistent with current data and mildly favored when SNe Ia are included, making it a viable extension of $\Lambda$CDM that merits further investigation with future high precision measurements.