Observational constraints on interactions between dark energy and dark matter with momentum and energy transfers

We place observational constraints on a dark energy (DE) model in which a quintessence scalar field φ is coupled to dark matter (DM) through momentum and energy exchanges. The momentum transfer is weighed by an interaction between the field derivative and DM four velocity with a coupling constant β, whereas the energy exchange is characterized by an exponential scalar-field coupling to the DM density with a coupling constant Q. A positive coupling β leads to the suppression for the growth of DM density perturbations at low redshifts, whose property offers a possibility for resolving the σ₈ tension problem. A negative coupling Q gives rise to a φ-matter-dominated epoch, whose presence can reduce the sound horizon around the cosmic microwave background (CMB) decoupling epoch. Using the data of the Planck 2018, 12th Sloan Digital Sky Survey, Phantheon supernovae samples, and 1-year dark energy survey, we find that the two couplings are constrained to be β=0.332_-0.237+1.246 and Q=-0.0312_-0.0085+0.0312 at a 68% confidence level (CL). Thus, there is an interesting observational signature of the momentum exchange (β≠0) between DE and DM, with a peak of the probability distribution of the energy transfer coupling at $Q<0$.