We use WMAP 9-year and other CMB data to constrain cosmological models where the primordial perturbations have both an adiabatic and a (possibly correlated) neutrino density (NDI), neutrino velocity (NVI), or cold dark matter density (CDI) isocurvatu
re component. For NDI and CDI we use both a phenomenological approach, where primordial perturbations are parametrized in terms of amplitudes at two scales, and a slow-roll two-field inflation approach, where slow-roll parameters are used as primary parameters. For NVI we use only the phenomenological approach, since it is difficult to imagine a connection with inflation. We find that in the NDI and NVI cases larger isocurvature fractions are allowed than in the corresponding models with CDI. For uncorrelated perturbations, the upper limit to the primordial NDI (NVI) fraction is 24% (20%) at k = 0.002 Mpc^{-1} and 28% (16%) at k = 0.01 Mpc^{-1}. For maximally correlated (anticorrelated) perturbations, the upper limit to the NDI fraction is 3.0% (0.9%). The nonadiabatic contribution to the CMB temperature variance can be as large as 10% (-13%) for the NDI (NVI) modes. Bayesian model comparison favors pure adiabatic initial mode over the mixed primordial adiabatic and NDI, NVI, or CDI perturbations. At best, the betting odds for a mixed model (uncorrelated NDI) are 1:3.4 compared to the pure adiabatic model. For the phenomenological generally correlated mixed models the odds are about 1:100, whereas the slow-roll approach leads to 1:13 (NDI) and 1:51 (CDI).
We constrain cosmological models where the primordial perturbations have both an adiabatic and a (possibly correlated) cold dark matter (CDM) or baryon isocurvature component. We use both a phenomenological approach, where the primordial power spectr
a are parametrized with amplitudes and spectral indices, and a slow-roll two-field inflation approach where slow-roll parameters are used as primary parameters. In the phenomenological case, with CMB data, the upper limit to the CDM isocurvature fraction is alpha<6.4% at k=0.002Mpc^{-1} and 15.4% at k=0.01Mpc^{-1}. The median 95% range for the non-adiabatic contribution to the CMB temperature variance is -0.030<alpha_T<0.049. Including the supernova (or large-scale structure, LSS) data, these limits become: alpha<7.0%, 13.7%, and -0.048<alpha_T< 0.042 (or alpha<10.2%, 16.0%, and -0.071<alpha_T<0.024). The CMB constraint on the tensor-to-scalar ratio, r<0.26 at k=0.01Mpc^{-1}, is not affected by the nonadiabatic modes. In the slow-roll two-field inflation approach, the spectral indices are constrained close to 1. This leads to tighter limits on the isocurvature fraction, with the CMB data alpha<2.6% at k=0.01Mpc^{-1}, but the constraint on alpha_T is not much affected, -0.058<alpha_T<0.045. Including SN (or LSS) data, these limits become: alpha< 3.2% and -0.056<alpha_T<0.030 (or alpha<3.4% and -0.063<alpha_T<-0.008). When all spectral indices are close to each other the isocurvature fraction is somewhat degenerate with the tensor-to-scalar ratio. In addition to the generally correlated models, we study also special cases where the perturbation modes are uncorrelated or fully (anti)correlated. We calculate Bayesian evidences (model probabilities) in 21 different cases for our nonadiabatic models and for the corresponding adiabatic models, and find that in all cases the data support the pure adiabatic model.
