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We constrain cosmological models where the primordial perturbations have bothan adiabatic and a (possibly correlated) cold dark matter (CDM) or baryonisocurvature component. We use both a phenomenological approach, where theprimordial power spectra are parametrized with amplitudes and spectral indices,and a slow-roll two-field inflation approach where slow-roll parameters areused as primary parameters. In the phenomenological case, with CMB data, theupper 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-adiabaticcontribution to the CMB temperature variance is -0.030<\alpha_T<0.049.Including the supernova (or large-scale structure, LSS) data, these limitsbecome: \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 theslow-roll two-field inflation approach, the spectral indices are constrainedclose to 1. This leads to tighter limits on the isocurvature fraction, with theCMB data \alpha<2.6% at k=0.01Mpc^{-1}, but the constraint on \alpha_T is notmuch affected, -0.058<\alpha_T<0.045. Including SN (or LSS) data, these limitsbecome: \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 theisocurvature fraction is somewhat degenerate with the tensor-to-scalar ratio.In addition to the generally correlated models, we study also special caseswhere the perturbation modes are uncorrelated or fully (anti)correlated. Wecalculate Bayesian evidences (model probabilities) in 21 different cases forour nonadiabatic models and for the corresponding adiabatic models, and findthat in all cases the data support the pure adiabatic model.

astrophysical journal/the astrophysical journal

Constraints on scalar and tensor perturbations in phenomenological and  two-field inflation models: Bayesian evidences for primordial isocurvature  and tensor modes