Bounds on cold dark matter and neutrino isocurvature perturbations from CMB and LSS data

Early universe models for the origin of structure typically produce 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 13 free parameters, including independent spectral indexes for each of the modes and for their cross-correlation angle. We find that around a pivot wave number of k=0. 05h Mpc^-1 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 two 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- forests, but then obtain large blue spectral indexes for the nonadiabatic contributions. We also translate our bounds in terms of constraints on double inflation models with two uncoupled massive fields.