Constraining Interactions in Cosmology's Dark Sector

We consider the cosmological constraints on theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the universe, in light of the most recent supernovae, large scale structure and cosmic microwave background data. For a variety of models, we show that the strength of the coupling of dark matter to a quintessence field is constrained to be less than 7% of the coupling to gravity. We also show that long range interactions between fermionic dark matter particles mediated by a light scalar with a Yukawa coupling are constrained to be less than 5% of the strength of gravity at a distance scale of 10 Mpc. We show that all of the models we consider are quantum mechanically weakly coupled, and argue that some other models in the literature are ruled out by quantum mechanical strong coupling.