  In standard cosmologies, dark energy interacts only gravitationally with dark
matter. There could be a non-gravitational interaction in the dark sector,
leading to changes in the effective DE equation of state, in the redshift
dependence of the DM density and in structure formation. We use CMB, BAO and
SNIa data to constrain a model where the energy transfer in the dark sector is
proportional to the DE density. There are two subclasses, defined by the
vanishing of momentum transfer either in the DM or the DE frame. We conduct a
Markov-Chain Monte-Carlo analysis to obtain best-fit parameters. The background
evolution allows large interaction strengths, and the constraints from CMB
anisotropies are weak. The growth of DM density perturbations is much more
sensitive to the interaction, and can deviate strongly from the standard case.
However, the deviations are degenerate with galaxy bias and thus more difficult
to constrain. Interestingly, the ISW signature is suppressed since the
non-standard background evolution can compensate for high growth rates. We also
discuss the partial degeneracy between interacting DE and modified gravity, and
how this can be broken.
