Correlated primordial perturbations in light of CMB and large scale structure data

We use cosmic microwave background (CMB) and large scale structure data to constrain cosmological models where the primordial perturbations have both an adiabatic and a cold dark matter (CDM) isocurvature component. We allow for a possible correlation between the adiabatic and isocurvature modes, and for different spectral indices for the power in each mode and for their correlation. We do a likelihood analysis with 11 independent parameters and discuss the effect of choosing the pivot scale for the definition of amplitude parameters. The upper limit to the isocurvature fraction is 18% around a pivot scale $k=0.01\text{ }\text{ }{\mathrm{M}\mathrm{p}\mathrm{c}}^{\ensuremath{-}1}$. For smaller pivot wavenumbers the limit stays about the same. For larger pivot wavenumbers, very large values of the isocurvature spectral index are favored, which makes the analysis problematic, but larger isocurvature fractions seem to be allowed. For large isocurvature spectral indices ${n}_{\mathrm{i}\mathrm{s}\mathrm{o}}>2$ a positive correlation between the adiabatic and isocurvature mode is favored, and for ${n}_{\mathrm{i}\mathrm{s}\mathrm{o}}<2$ a negative correlation is favored. The upper limit to the nonadiabatic contribution to the CMB temperature variance is 7.5%. Of the standard cosmological parameters, determination of the CDM density ${\ensuremath{\omega}}_{c}$ and the sound horizon angle $\ensuremath{\theta}$ (or the Hubble constant ${H}_{0}$) are affected most by a possible presence of a correlated isocurvature contribution. The baryon density ${\ensuremath{\omega}}_{b}$ nearly retains its ``adiabatic value''.