Constraints on interacting dark energy with a constant equation of state in light of DESI DR2: The role of the interaction term

Recent DESI baryon acoustic oscillation (BAO) analyses suggest a preference for an evolving dark energy equation of state (EoS) that crosses the phantom divide $w=-1$. Interactions between dark energy and dark matter can also produce an apparent phantom-divide crossing in the effective dark energy EoS. In this work, we investigate interacting dark energy (IDE) models with a constant EoS parameter $w$, using cosmic microwave background (CMB) observations from Planck, ACT, and SPT, DESI DR2 BAO measurements, and type Ia supernova data from PantheonPlus, DES-Dovekie, and DESY5. We consider four typical forms of the interaction term $Q$. Our results show that the IDE models with $Q\propto {\rho }_{\mathrm{d}\mathrm{e}}$ generally exhibit a stronger preference for nonzero dark-sector interactions. In particular, for the CMB+DESI+DES-Dovekie data, the IDE model with $Q=\beta H_0{\rho }_{\mathrm{d}\mathrm{e}}$ yields $\beta =-2.52_{-0.54}^{+0.80}$ and $w=-1.510_{-0.120}^{+0.170}$, corresponding to deviations from $\beta =0$ and $w=-1$ at the $3.2\sigma$ and $3.0\sigma$ levels, respectively. Interestingly, the effective EoS of the IDE model with $Q=\beta H_0{\rho }_{\mathrm{d}\mathrm{e}}$ exhibits a redshift evolution resembling that of the $w_0{w}_a$CDM model, crossing the phantom divide. Bayesian evidence further indicates that this IDE model is favored over $\mathrm{\Lambda }$CDM and the other three IDE models. Our analysis helps identify which interaction forms better account for current cosmological observations.