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 ($w=-1$), which, if confirmed with significance $>5σ$, will falsify the $Λ$CDM model. We explore a generalized formulation of an emergent dark energy (GEDE) model and test its viability using multiple observational datasets, including Baryon Acoustic Oscillation (BAO) measurements from the DESI DR2 release, the Type Ia Supernovae (SNe Ia) compilation, and Cosmic Microwave Background (CMB) distance priors. Through this analysis, we place joint constraints on the dark energy equation of state $w$ and the redshift-dependent energy density function $f_{DE}(z)$, which exhibits behavior consistent with a quintessence. Specifically, $w(0) = -0.820$ with DESI DR2 + CMB, $-0.845$ with DESI DR2 + CMB + PP$^+$, $-0.828$ with DESI DR2 + CMB + Union3, and $-0.804$ with DESI DR2 + CMB + DESY5. Across multiple combinations of datasets, we observe a recurring trend toward negative values of the GEDE parameter $Δ$. The negative value of $Δ$ favors the injection of dark energy at earlier redshift with $z_t$ close to 0.5. We conduct a comparative analysis between the GEDE and $Λ$CDM models using different BAO scale. Within current observational uncertainties, our results position the GEDE framework as a viable and promising alternative, meriting further investigation. The effectiveness of the model is quantitatively assessed using the Bayes factor.