We use observations of cosmic microwave background anisotropies , supernova luminosities and the baryon acoustic oscillation signal in the galaxy distribution to constrain the cosmological parameters in a simple interacting dark energy model with a time-varying equation of state .
Using a Monte Carlo Markov Chain technique we determine the posterior likelihoods .
Constraints from the individual data sets are weak , but the combination of the three data sets confines the interaction constant \Gamma to be less than 23 % of the expansion rate of the Universe H _ { 0 } ; at 95 % CL -0.23 < \Gamma / H _ { 0 } < +0.15 .
The CMB acoustic peaks can be well fitted even if the interaction rate is much larger , but this requires a larger or smaller ( depending on the sign of interaction ) matter density today than in the non-interacting model .
Due to this degeneracy between the matter density and the interaction rate , the only observable effect on the CMB is a larger or smaller integrated Sachs–Wolfe effect .
While SN or BAO data alone do not set any direct constraints on the interaction , they exclude the models with very large matter density , and hence indirectly constrain the interaction rate when jointly analysed with the CMB data .
To enable the analysis described in this paper , we present in a companion paper [ arXiv:0907.4981 ] a new systematic analysis of the early radiation era solution to find the adiabatic initial conditions for the Boltzmann integration .