Constraints on primordial isocurvature perturbations and spatial
  curvature by Bayesian model selection
  We present posterior likelihoods and Bayesian model selection analysis for
generalized cosmological models where the primordial perturbations include
correlated adiabatic and cold dark matter isocurvature components. We perform
nested sampling with flat and, for the first time, curved spatial geometries of
the Universe, using data from the cosmic microwave background (CMB)
anisotropies, the Union supernovae (SN) sample and a combined measurement of
the integrated Sachs-Wolfe (ISW) effect. The CMB alone favors a 3% (positively
correlated) isocurvature contribution in both the flat and curved cases. The
non-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 CMB
with SN data artificially biases the result towards the pure adiabatic LCDM
concordance model, whereas in the curved case the favored level of
non-adiabaticity stays at 3% level with all combinations of data. However, the
ratio of Bayes factors, or Delta ln(evidence), is more than 5 points in favor
of the flat adiabatic LCDM model, which suggests that the inclusion of the 5
extra parameters of the curved isocurvature model is not supported by the
current data. The results are very sensitive to the second and third acoustic
peak regions in the CMB temperature angular power: therefore a careful
calibration of these data will be required before drawing decisive conclusions
on the nature of primordial perturbations. Finally, we point out that the odds
for the flat non-adiabatic model are 1:3 compared to the curved adiabatic
model. This may suggest that it is not much less motivated to extend the
concordance model with 4 isocurvature degrees of freedom than it is to study
the spatially curved adiabatic model.
