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

In multi-field inflation models, correlated adiabatic and isocurvature fluctuations are produced and in addition to the usual adiabatic fluctuation with a spectral index n_ad1 there is another adiabatic component with a spectral index n_ad2 generated by entropy perturbation during inflation, if the trajectory in the field space is curved. Allowing n_ad1 and n_ad2 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 n_iso < 1.84 for the isocurvature spectral index gives fiso < 0.84 for the isocurvature fraction of the initial power spectrum at k_0 = 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.