When Dark Energy Turns On: Constraints on a Critical Emergence Model

Abstract: We investigate a specific emergent dark energy scenario, known as critically emergent dark energy (CEDE), in which dark energy is effectively absent in the early Universe and becomes dynamically relevant only after a critical cosmic epoch through a phase transition. We constrain this model using recent cosmological observations, including cosmic microwave background (CMB) data from \emph{Planck} 2018, baryon acoustic oscillation (BAO) measurements from SDSS and DESI DR2, and two independent Type Ia supernova compilations, PantheonPlus and Union3. Our results show that within the CEDE framework a dark energy phase transition is not ruled out. In particular, CMB-only, CMB+SDSS, and CMB+DESI datasets provide evidence for a nonzero transition scale factor and, according to standard statistical indicators such as $Δχ^2$ and Bayesian evidence, can favor CEDE over the $Λ$CDM model. At the same time, we find that CEDE does not fully resolve the Hubble constant tension. Overall, our analysis indicates that dark energy models featuring a phase transition remain a viable and phenomenologically interesting extension of the standard cosmological framework. Upcoming high-precision cosmological surveys will be essential to further assess whether such emergent dark energy scenarios represent a genuine departure from $Λ$CDM or an effective description of current data.