How dark sector equations of state govern interaction signatures

Using late-Universe observations, we demonstrate that freeing dark energy and dark matter equations of state (EoS) dramatically alters the inferred strength and direction of their interactions. When dark sector EoS are fixed to $w_{\mathrm{de}}=-1$ and $w_{\mathrm{dm}}=0$, the data consistently favor an energy transfer from dark energy to dark matter across various interaction forms. This apparent evidence, however, proves highly sensitive to the EoS assumptions: treating $w_{\mathrm{de}}$ as a free parameter substantially weakens the evidence for interaction, with its value converging to the quintessence regime ($w_{\mathrm{de}}>-1$). In contrast, freeing $w_{\mathrm{dm}}$ maintains a preference for interaction, revealing a correlation where positive $w_{\mathrm{dm}}$ is associated with energy transfer from dark energy to dark matter, and negative $w_{\mathrm{dm}}$ with energy transfer from dark matter to dark energy. These findings caution against the simplistic assumption of $Λ$CDM EoS values when attempting to detect a possible interaction. Despite these fundamental degeneracies, model comparison indicates that interacting dark energy scenarios are positively to strongly supported by AIC and DIC, but only inconclusively to weakly supported by Bayesian evidence against the $Λ$CDM model.