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

We constrain cosmological models where the primordial perturbations have an adiabatic and a (possibly correlated) cold dark matter (CDM) or baryon isocurvature component. We use both a phenomenological approach, where the power spectra of primordial perturbations are parameterized with amplitudes and spectral indices, and a slow-roll two-field inflation approach where slow-roll parameters are used as primary parameters, determining the spectral indices and the tensor-to-scalar ratio. In the phenomenological case, with CMB data, the upper limit to the CDM isocurvature fraction is α < 6.4% at k = 0.002 Mpc^-1 and 15.4% at k = 0.01 Mpc^-1. The non-adiabatic contribution to the CMB temperature variance is -0.030 < α_T < 0.049 at the 95% confidence level. Including the supernova (SN) (or large-scale structure) data, these limits become α < 7.0%, 13.7%, and -0.048 < α_T < 0.042 (or α < 10.2%, 16.0%, and -0.071 < α_T < 0.024). The CMB constraint on the tensor-to-scalar ratio, r < 0.26 at k = 0.01 Mpc^-1, is not affected by the non-adiabatic 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 α < 2.6% at k = 0.01 Mpc^-1, but the constraint on α_T is not much affected, -0.058 < α_T < 0.045. Including SN (or LSS) data, these limits become α < 3.2% and -0.056 < α_T < 0.030 (or α < 3.4% and -0.063 < α_T < -0.008). In addition to the generally correlated models, we study also special cases where the adiabatic and isocurvature modes are uncorrelated or fully (anti)correlated. We calculate Bayesian evidences (model probabilities) in 21 different non-adiabatic cases and compare them to the corresponding adiabatic models, and find that in all cases the data support the pure adiabatic model.