Probing the Type 3 interacting dark-energy model using matter pairwise velocity

Dark sector interactions can be explored via the so-called Type 3 model where dark matter and dark energy exchange momentum only, so as to minimize deviations from the $Λ$CDM background expansion history. Using N-body simulations, we analyze the imprint of Type 3 model parameters, the momentum exchange coupling constant $β$ and the slope of scalar field potential $λ$, on large-scale structure (LSS) observables, particularly the matter pairwise velocity statistics. We find that the effects of $β$ ($< 0$) and $λ$ on the mean matter peculiar pairwise velocity and velocity dispersion are degenerate. Our results highlight the potential of velocity statistics as a probe of dark sector interactions and underscore the importance of disentangling $β$ and $λ$ in cosmological analyses.