Dark sector interactions in the $w \rightarrow -1$ limit: velocity locking in pure momentum exchange models
Models of interacting dark energy (DE) and dark matter (DM) involving pure momentum exchange are a promising avenue for resolving cosmological tensions. However, the behaviour of these interactions in the theoretically challenging limit where the DE equation of state, $w$, approaches $-1$ is not fully understood. We demonstrate that a generic feature of these models is a $w$-dependent velocity-locking mechanism, which systematically shifts the onset of matter power spectrum suppression to smaller scales as $w \rightarrow -1$. The suppression magnitude depends on the difference in fluid velocities. In this limit, however, the interaction's drag dominates over the DE pressure support and causes the DE velocity to track that of the DM fluid at larger scales. This mechanism provides a physical explanation for the weaker constraints found in the literature when $w\approx-1$ in models where the interaction strength does not explicitly depend on $w$. We also demonstrate that the common approximation of neglecting DE perturbations ($\delta_{\mathrm{DE}}=\theta_{\mathrm{DE}}=0$) fails in this limit. By artificially increasing the velocity difference between the fluids, this simplification incorrectly removes the $w$-dependent velocity-locking mechanism and erases the shift in power spectrum suppression to smaller scales. This leads to an overestimation of the constraining power of cosmological data on the interaction strength.