  We investigate cosmological constraints on primordial isocurvature and tensor
perturbations, using recent observations of the cosmic microwave background and
the large scale structure. We find that present observations are consistent
with purely adiabatic initial conditions for the structure formation under any
priors on correlations of isocurvature modes, and upper limits on the
contribution of isocurvature and tensor perturbations are presented. We also
apply the obtained constraints to some specific theoretical models, axion
isocurvature perturbation models and curvaton models, and give some
implications for theoretical models.
