Simplest inflationary models with one scalar field produce nearly scale invariant adiabatic "initial" perturbations. This means that the total energy density fluctuates but the specific entropy remains spatially constant. More generally, there may be also another initial mode called isocurvature perturbation. In this case the particle number densities fluctuate implying entropy fluctuation. For example, fluctuation in (cold dark) matter energy density could be compensated by opposite fluctuation in photon energy density so that there is no fluctuation in total energy density and thus the spatial curvature is constant. (E.g. inflation with more than one scalar field or original axion model give rise to isocurvature initial perturbations.) Because no generally accepted theory of inflation exists, it is natural to consider both adiabatic and isocurvature perturbations being equally probable. As is obvious, the nature of initial perturbations depends crucially on the underlying particle physics. Most probably the initial perturbations (from which the observed structure of the universe and the temperature anisotropies seen in the cosmic microwave background radiation are evolved) will be a mixture of adiabatic and isocurvature fluctuations.

In the recent balloon borne experiments, the anisotropies in the cosmic microwave background radiation have been measured up to so small angular scales that at least the first two of so called acoustic peaks (in the angular power spectrum) are now clearly detected. The position of these, many years ago theoretically predicted, peaks can be used to distinguish between adiabatic and isocurvature fluctuations as well as to decide whether the geometry of the universe is flat or curved. Moreover, the angular power spectrum can be used to extract cosmological parameters such as baryon density, cold dark matter density, cosmological constant and matter density with unprecedented accuracy. Nearly scale invariant adiabatic models with flat geometry of the universe fit incredibly well to the CMB data. However, this should not be taken as a proof that all pure isocurvature models are ruled out. Some unconventional combination of cosmological parameters, e.g. $\Omega\ne 1$ and a spectrum with a large tilt, could at least in principle give equally good fit as the adiabatic models. To check this possibility we have considered pure isocurvature cold dark matter (CDM) models in the case of open and closed universe. We have allowed for a very wide range of cosmological parameters to find the best fit to the COBE, Boomerang and Maxima-1 data. Taking into account constraints from large-scale structure and big bang nucleosynthesis, we have found a best fit with $\chi^2 = 121$, which is to be compared to $\chi^2 = 44$ of a flat adiabatic "reference model". This means that the current data strongly disfavour pure isocurvature perturbations. Hence a common claim that the data imply a flat geometry and scale invariant adiabatic initial fluctuations really seems to be justified. Of course, a mixture of adiabatic and isocurvature fluctuations with minor power around the first acoustic peak coming from isocurvature fluctuations remains allowed. Accordingly, such particle physics (or particle cosmology) models which produce only mainly CDM isocurvature fluctuations are ruled out. Typical example of this kind of excluded model is the original axion model, where the present CDM is made of axions, which "carry" isocurvature perturbation. However, recently the pre-big bang with suitably decaying axions has shown to be able to produce adiabatic fluctuations with nearly scale invariant spectrum and thus the axions may be rescued.