Constraints on the interaction and self-interaction of dark energy from   cosmic microwave background
  It is well-known that even high quality cosmic microwave background (CMB) observations are not sufficient on their own to determine the equation of state of the dark energy, due to the effect of the so-called geometric degeneracy at large multipoles and the cosmic variance at small ones. In contrast, we find that CMB data can put tight constraints on another fundamental property of the dark energy, namely its coupling to dark matter. We compare the current high-resolution CMB data to models of dark energy characterized by an inverse power law or exponential potential and by the coupling to dark matter. We determine the curve of degeneracy between the dark energy equation of state and the dimensionless Hubble parameter h and show that even an independent perfect determination of h may be insufficient to distinguish dark energy from a pure cosmological constant with the current dataset. On the other hand, we find that the interaction with dark matter is firmly bounded, regardless of the potential. In terms of the dimensionless ratio \beta of the dark energy interaction to gravity, we find \beta <0.16 (95% c.l.). This implies that the effective equation of state between equivalence and tracking has been close to the pure matter equation of state within 1% and that scalar gravity is at least 40 times weaker than tensor gravity. Further, we show that an experiment limited by cosmic variance only, like the Planck mission, can put an upper bound \beta < 0.05 (95% c.l.). This shows that CMB observations have a strong potentiality not only as a test of cosmic kinematics but also as a gravitational probe. 
Luca Amendola, Claudia Quercellini, Domenico Tocchini-Valentini and   Alessandro Pasqui (INAF-Osservatorio Astronomico di Roma)