On phenomenological models of dark energy interacting with dark matter

TL;DR

The paper argues that phenomenological couplings between dark energy and dark matter likely modify not only the background energy exchange but also the gravitational dynamics through a bulk dissipative pressure $\pi$, with potential implications for structure formation. By deriving background equations from a total Lagrangian and exploring covariant formulations, it shows that a consistent treatment requires accounting for new terms beyond simple $Q$-type exchanges, and that a Lagrangian-based approach (e.g., Scalar-Fluid theories) provides a coherent framework where $\pi$ and $Q_{\nu}$ are explicitly linked to dark-sector degrees of freedom. The work highlights fundamental ambiguities in perturbation theory for phenomenological models and advocates for effective actions to define covariant couplings, tying the observed phenomenology to deeper theoretical structure. Overall, the paper clarifies how dark-sector interactions can influence both cosmic expansion and structure growth, and emphasizes the need for a fundamental description to avoid ambiguities in cosmological perturbations.

Abstract

An interaction between dark matter and dark energy is usually introduced by a phenomenological modification of the matter conservation equations, while the Einstein equations are left unchanged. Starting from some general and fundamental considerations, in this work it is shown that a coupling in the dark sector is likely to introduce new terms also in the gravitational dynamics. Specifically in the cosmological background equations a bulk dissipative pressure, characterizing viscous effects and able to suppress structure formation at small scales, should appear from the dark coupling. At the level of the perturbations the analysis presented in this work reveals instead the difficulties in properly defining the dark sector interaction from a phenomenological perspective.