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We use observations of cosmic microwave background (CMB) 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 Γ to be less than 23 per cent of the expansion rate of the Universe  H  0 ; at 95 per cent confidence level  −0.23 &lt; Γ/ H  0  &lt; +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 supernova or baryon acoustic oscillation 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, a new systematic analysis of the early radiation era solution to find the adiabatic initial conditions for the Boltzmann integration.

Observational constraints on an interacting dark energy model