Open and closed CDM isocurvature models contrasted with the CMB data

We consider pure isocurvature cold dark matter models in the case of open and closed universes. We allow for a large spectral tilt and scan the six-dimensional parameter space for the best fit to the COBE, Boomerang, and Maxima-1 data. Taking into account constraints from large-scale structure and big bang nucleosynthesis, we find a best fit with ${\chi }^2=121,$ which is to be compared to ${\chi }^2=44\mathrm{}$ of a flat adiabatic reference model. Hence the current data strongly disfavor pure isocurvature perturbations.