Correlated adiabatic and isocurvature CMB fluctuations in the light of the WMAP data

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In multi-field inflation models, correlated adiabatic and isocurvature fluctuations are produced and in addition to the usual adiabatic fluctuation with a spectral index nₐd1 there is another adiabatic component with a spectral index nₐd2 generated by entropy perturbation during inflation, if the trajectory in the field space is curved. Allowing nₐd1 and nₐd2 to vary independently we find that the WMAP data favour models where the two adiabatic components have opposite spectral tilts. This leads naturally to a running adiabatic spectral index. The WMAP data with a prior nᵢso < 1.84 for the isocurvature spectral index gives fiso < 0.84 for the isocurvature fraction of the initial power spectrum at k₀ = 0.05 Mpc⁻¹. We also comment on a 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 would need a large tau to fit the TE spectrum.