  Generic models for the origin of structure predict a spectrum of initial
fluctuations with a mixture of adiabatic and isocurvature perturbations. Using
the observed anisotropies of the cosmic microwave backgound, the matter power
spectra from large scale structure surveys and the luminosity distance vs
redshift relation from supernovae of type Ia, we obtain strong bounds on the
possible cold dark matter/baryon as well as neutrino isocurvature contributions
to the primordial fluctations in the Universe. Neglecting the possible effects
of spatial curvature and tensor perturbations, we perform a Bayesian likelihood
analysis with thirteen free parameters, including independent spectral indexes
for each of the modes and for their cross-correlation angle. We find that
around a pivot wavenumber of k=0.05 h/Mpc the amplitude of the correlated
isocurvature component cannot be larger than about 60% for the cold dark matter
mode, 40% for the neutrino density mode, and 30% for the neutrino velocity
mode, at 2 sigma. In the first case, our bound is larger than the WMAP
first-year result, presumably because we prefer not to include any data from
Lyman-alpha forests, but then obtain large blue spectral indexes for the
non-adiabatic contributions. We also translate our bounds in terms of
constraints on double inflation models with two uncoupled massive fields.
