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 power spectra of primordial perturbations are parametrized 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 cosmic microwave background ( CMB ) data , the upper limit to the CDM isocurvature fraction \alpha is 6.4 % at k = 0.002 Mpc ^ { -1 } and 15.4 % at k = 0.01 Mpc ^ { -1 } .
At smaller scales ( larger k ) larger isocurvature fractions are allowed , and therefore large values of the isocurvature spectral index , n _ { \mathrm { iso } } \approx 2 , are formally favored .
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 \lesssim 0.26 at k = 0.01 Mpc ^ { -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 = 0.01 Mpc ^ { -1 } , but since the non-adiabatic contribution to the CMB temperature variance comes mostly from larger scales its median 95 % range is not much affected , -0.058 < \alpha _ { T } < 0.045 .
Including supernova ( 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 adiabatic and isocurvature 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 current data support the pure adiabatic model .