Late-Time Emergence of Dark Energy and Its Interaction with Dark Matter
We present an interacting scenario between dark energy (DE) and dark matter (DM), where DE has an emergent nature, that means, DE was absent in the early universe but it becomes effective only at late times. We consider two specific emergent DE models, one with no free parameters and the other featuring two parameters describing the speed and epoch of the transition. We constrain both scenarios using the cosmic microwave background (CMB) measurements from the Planck 2018 release, baryon acoustic oscillations from DESI DR2, and three different compilations of Type Ia supernovae (PantheonPlus, DES-Dovekie, and Union3). Our analysis indicates that current cosmological probes are not able to tightly constrain the speed of the transition. For both scenarios, the posterior distribution of the interaction parameter is shifted away from zero at more than 95\% CL whenever the CMB data are combined with any of these additional probes, with the preferred direction corresponding to a transfer of energy from DE to DM. While CMB alone yields a high value of $H_0$, in agreement with local determinations, this effect is reduced when DESI is added and disappears once supernova data are included. In contrast, the clustering parameter $S_8$ is consistently shifted toward lower values in the combined datasets, and it is correlated with the preference for a negative interaction. However, according to the $Δχ^2_{\rm min}$ and Bayesian evidence, none of the interacting models is favored over $Λ$CDM or $w_0w_a$CDM, indicating that the interaction does not rescue these emergent DE models. Our results therefore highlight the limitations of these scenarios in addressing current cosmological tensions, while pointing to the crucial role of future data in further assessing their viability.