Correlated Adiabatic and Isocurvature Cosmic Microwave Background Fluctuations in the Wake of the Results from the Wilkinson Microwave Anisotropy Probe

In general correlated models, in addition to the usual adiabatic component with a spectral index ${n}_{\mathrm{a}\mathrm{d}\mathrm{1}}$ there is another adiabatic component with a spectral index ${n}_{\mathrm{a}\mathrm{d}\mathrm{2}}$ generated by entropy perturbation during inflation. We extend the analysis of a correlated mixture of adiabatic and isocurvature cosmic microwave background fluctuations of the Wilkinson Microwave Anisotropy Probe (WMAP) group, who set the two adiabatic spectral indices equal. Allowing ${n}_{\mathrm{a}\mathrm{d}\mathrm{1}}$ and ${n}_{\mathrm{a}\mathrm{d}\mathrm{2}}$ 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 $2\ensuremath{\sigma}$ upper bound for the isocurvature fraction ${f}_{\mathrm{i}\mathrm{s}\mathrm{o}}$ of the initial power spectrum at ${k}_{0}=0.05\text{ }{\mathrm{M}\mathrm{p}\mathrm{c}}^{\ensuremath{-}1}$ increases somewhat, e.g., from 0.76 of ${n}_{\mathrm{a}\mathrm{d}\mathrm{2}}={n}_{\mathrm{a}\mathrm{d}\mathrm{1}}$ models to 0.84 with a prior ${n}_{\mathrm{i}\mathrm{s}\mathrm{o}}<1.84$ for the isocurvature spectral index.