Correlated adiabatic and isocurvature CMB fluctuations in the wake of the WMAP

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In general correlated models, in addition to the usual adiabatic component with a spectral index nₐd1 there is another adiabatic component with a spectral index nₐd2 generated by entropy perturbation during inflation. We extend the analysis of a correlated mixture of adiabatic and isocurvature CMB fluctuations of the WMAP group, who set the two adiabatic spectral indices equal. Allowing nₐd1 and nₐd2 to vary independently we find that the WMAP data favor models where the two adiabatic components have opposite spectral tilts. Using the WMAP data only, the 2-sigma upper bound for the isocurvature fraction fᵢso of the initial power spectrum at k₀=0.05 Mpc⁻¹ increases somewhat, e.g., from 0.76 of nₐd2 = nₐd1 models to 0.84 with a prior nᵢso < 1.84 for the isocurvature spectral index. We also comment on a possible degeneration between the correlation component and the optical depth tau. Moreover, the measured low quadrupole in the TT angular power could be achieved by a strong negative correlation, but then one needs a large tau to fit the TE spectrum.