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We present posterior likelihoods and Bayesian model selection analysis forgeneralized cosmological models where the primordial perturbations includecorrelated adiabatic and cold dark matter isocurvature components. We performnested sampling with flat and, for the first time, curved spatial geometries ofthe Universe, using data from the cosmic microwave background (CMB)anisotropies, the Union supernovae (SN) sample and a combined measurement ofthe integrated Sachs-Wolfe (ISW) effect. The CMB alone favors a 3% (positivelycorrelated) isocurvature contribution in both the flat and curved cases. Thenon-adiabatic contribution to the observed CMB temperature variance is 0 <alpha_T < 7% at 98% CL in the curved case. In the flat case, combining the CMBwith SN data artificially biases the result towards the pure adiabatic LCDMconcordance model, whereas in the curved case the favored level ofnon-adiabaticity stays at 3% level with all combinations of data. However, theratio of Bayes factors, or Delta ln(evidence), is more than 5 points in favorof the flat adiabatic LCDM model, which suggests that the inclusion of the 5extra parameters of the curved isocurvature model is not supported by thecurrent data. The results are very sensitive to the second and third acousticpeak regions in the CMB temperature angular power: therefore a carefulcalibration of these data will be required before drawing decisive conclusionson the nature of primordial perturbations. Finally, we point out that the oddsfor the flat non-adiabatic model are 1:3 compared to the curved adiabaticmodel. This may suggest that it is not much less motivated to extend theconcordance model with 4 isocurvature degrees of freedom than it is to studythe spatially curved adiabatic model.

Constraints on primordial isocurvature perturbations and spatial curvature by Bayesian model selection