A microphysically inspired approach to dark matter-dark energy interactions: first bounds on dark-sector scattering cross sections

The observational tension regarding the value of the Hubble constant ($H_0$) has motivated the exploration of alternative cosmological scenarios, including Interacting Dark Energy models. However, the majority of IDE models studied in the literature rely on phenomenological interaction terms proportional to the Hubble parameter (e.g., $Q\propto H\rho$), which lack a clear microphysical justification and often suffer from large-scale instabilities. In this work, we propose and investigate a "bottom-up" IDE model where the interaction is formulated directly from particle physics collision processes, taking the form $Q\propto\rho^2$. This interaction represents a reversible annihilation/creation process between Dark Matter and Dark Energy, motivated by the Boltzmann equation. We test this model against a combination of background cosmological data, Pantheon Plus, Cosmic Chronometers, DESI DR2, and CMB distance priors from Planck18. We find that the model is consistent with the data, yielding a Hubble constant of $H_0=67.71\pm0.65$ km s$^{-1}$ Mpc$^{-1}$ for the combined analysis. The dimensionless interaction rate coefficients are constrained to be small, with upper limits of $A < 7.586\times10^{-25}$ (for Dark Matter self annihilation) and $B < 0.048$ (for Dark Energy self annihilation) at 95\% confidence level. Since the interaction model is parameterized by the expansion rate, these bounds on $H_0$, $A$, and $B$ directly translate into a strict limit on the thermally-averaged annihilation cross-section per unit of mass. The constraints on the coupling $A$ imply that, if such a collisional interaction exists, the effective dark-matter annihilation cross section per unit mass is highly suppressed relative to the cosmological expansion rate. In contrast, the corresponding dark-energy contribution, governed by $B$, is only constrained at the level of a few percent in dimensionless units.