Testing the Direction of Dark Sector Interaction Using Late-Time Datasets

In this work, we constrain the phenomenological interacting dark energy $\xi$IDE model using baryon acoustic oscillation measurements from DESI Data Release 1 and Data Release 2, combined with cosmic chronometer measurements, compressed CMB likelihoods, and three different Type Ia supernova compilations: Pantheon$^+$, DES-Dovekie, and Union3. We constrain the parameters of the $\xi$IDE model using a Markov Chain Monte Carlo analysis, using the nested sampling algorithm implemented in the \texttt{dynesty} package through the cosmological inference code \texttt{SimpleMC}. Compared to $\Lambda$CDM, the $\xi$IDE model favors slightly higher values of the Hubble constant, leading to a reduction in the Hubble tension. However, the tension is not completely resolved for any dataset combination. The parameter $\xi$ is consistently constrained to values close to its $\Lambda$CDM prediction, indicating no statistically significant deviation from the standard cosmological scenario. Similarly, except for the CMB + DESI DR1 + CC dataset combination, the dark energy equation-of-state parameter prefers values of $w_{\rm X}>-1$, showing a preference for quintessence-like behavior and providing evidence for dynamical dark energy. The interaction parameter combination, $\xi+3w_{\rm X}$, is found to be negative for all dataset combinations, corresponding to energy transfer from dark energy to dark matter. The strongest preference is obtained for the CMB + DESI DR2 + CC + Union3 dataset combination, yielding $\xi+3w_{\rm X}=-0.035\pm0.023$, which corresponds to a deviation of only $1.52\sigma$ from the non-interacting limit. Therefore, the current data provide only a weak indication of a non-zero dark-sector interaction. Model comparison based on the $N\sigma$ statistic shows weak evidence in favor of the interacting scenario, while Bayesian evidence consistently prefers the $\Lambda$CDM model.