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.
We study a model where two scalar fields, that are subdominant during inflation, decay into radiation some time after inflation has ended but before primordial nucleosynthesis. Perturbations of these two curvaton fields can be responsible for the pri
mordial curvature perturbation. We write down the full non-linear equations that relate the primordial perturbation to the curvaton perturbations on large scales, and solve them in a sudden-decay approximation. We calculate the power spectrum of the primordial perturbation, and finally go to second order to find the non-linearity parameter, fNL. Not surprisingly, we find large positive values of fNL if the energy densities of the curvatons are sub-dominant when they decay, as in the single curvaton case. But we also find a novel effect, which can be present only in multi-curvaton models: fNL becomes large even if the curvatons dominate the total energy density in the case when the inhomogeneous radiation produced by the first curvaton decay is diluted by the decay of a second nearly homogeneous curvaton. The minimum value min(fNL)=-5/4 which we find is the same as in the single-curvaton case. Using (non-)Gaussianity observations, Planck can be able to distinguish between single-field inflation and curvaton model. Hence it is important to derive theoretical predictions for curvaton model. From particle physics point of view it is more natural to assume multiple scalar fields (rather than just one ``curvaton in addition to inflaton). Our work updates the theoretical predictions of curvaton model to this case.
