Dark sector interactions in the $w ightarrow -1$ 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 ($δ_{\mathrm{DE}}=θ_{\mathrm{DE}}=0$) 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.

💡 Research Summary

This paper presents a groundbreaking analysis of interacting dark sector models, specifically focusing on pure momentum exchange between dark energy (DE) and dark matter (DM). As modern cosmology grapples with significant discrepancies known as the Hubble and $S_8$ tensions, the hypothesis of an interacting dark sector has emerged as a leading candidate to reconcile these observations. However, the dynamical behavior of these models in the critical limit where the dark energy equation of state, $w$, approaches $-1$ has remained largely enigmatic.

The authors identify a novel physical mechanism termed “velocity-locking” that emerges in the $w \to -1$ limit. They demonstrate that as $w$ approaches $-1$, the internal pressure support of the dark energy fluid diminishes, allowing the drag force resulting from the momentum exchange to become the dominant dynamical driver. This imbalance causes the velocity of the dark energy fluid to track the velocity of the dark matter fluid, effectively “locking” their velocities at larger scales.

This velocity-locking mechanism has profound implications for the observable matter power spectrum. The study shows that this mechanism systematically shifts the scale of matter power spectrum suppression toward smaller scales (higher wavenumbers $k$). This provides a robust physical explanation for why previous literature has reported significantly weaker constraints on the interaction strength when $w$ is near $-1$. It clarifies that the apparent weakness in constraints is not merely a result of observational limitations but is rooted in the fundamental change in the interaction’s physical manifestation.

Furthermore, the paper provides a critical critique of a widely used methodological approximation in cosmological studies: the assumption that dark energy perturbations ($\delta_{DE}$ and $\theta_{DE}$) can be neglected. The researchers prove that this simplification fails catastrophically in the $int w \to -1$ limit. By neglecting these perturbations, the velocity-locking mechanism is artificially erased, leading to an overestimation of the constraining power of cosmological data. This implies that current upper limits on the interaction strength between dark sectors might be artificially low due to this systematic error.

In conclusion, the study underscores the necessity of incorporating precise dark energy perturbations in future cosmological modeling. This work provides a vital theoretical foundation for upcoming high-precision cosmological surveys, ensuring that the next generation of observations can accurately probe the complex dynamics of the dark sector without the bias of erroneous approximations.