Correlated Primordial Perturbations in Light of CMB and LSS 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 an isocurvature component. We consider cold dark matter isocurvature perturbations only. 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. We discuss the effect of choosing the pivot scale for the definition of amplitude parameters. We obtain an upper limit of 18\% for the isocurvature fraction around a pivot scale $k = 0.01\mbox{ Mpc}^{-1}$. For smaller pivot wavenumbers the limit seems to stay 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 $\niso > 2$ a positive correlation between the adiabatic and isocurvature mode is favored, and for small $\niso < 2$ a negative correlation is favored. The upper limit to the nonadiabatic contribution to the CMB temperature variance is 7.5\%.