We use cosmic microwave background (CMB) and large scale structure data to constrain cosmological models where the primordial perturbations have both an adiabatic and a cold dark matter (CDM) isocurvature component. We allow for a possible correlation between the adiabatic and isocurvature modes, and for different spectral indices for the power in each mode and for their correlation. We do a likelihood analysis with 11 independent parameters and discuss the effect of choosing the pivot scale for the definition of amplitude parameters. The upper limit to the isocurvature fraction is 18% around a pivot scale k 0:01 Mpc ÿ1 . For smaller pivot wavenumbers the limit stays about the same. For larger pivot wavenumbers, very large values of the isocurvature spectral index are favored, which makes the analysis problematic, but larger isocurvature fractions seem to be allowed. For large isocurvature spectral indices n iso > 2 a positive correlation between the adiabatic and isocurvature mode is favored, and for n iso < 2 a negative correlation is favored. The upper limit to the nonadiabatic contribution to the CMB temperature variance is 7.5%. Of the standard cosmological parameters, determination of the CDM density ! c and the sound horizon angle (or the Hubble constant H 0 ) are affected most by a possible presence of a correlated isocurvature contribution. The baryon density ! b nearly retains its ''adiabatic value''.

The improved data on the cosmic microwave background (CMB) anisotropy allow a better determination of the adiabaticity of the primordial perturbation. Interestingly, we find that recent CMB data seem to favor a contribution of a primordial isocurvature mode where the entropy perturbation is positively correlated with the primordial curvature perturbation and has a large spectral index (n iso ∼ 3). With 4 additional parameters we obtain a better fit to the CMB data by ∆χ 2 = 9.7 compared to an adiabatic model. For this best-fit model the nonadiabatic contribution to the CMB temperature variance is 4%. According to a Markov Chain Monte Carlo analysis the nonadiabatic contribution is positive at more than 95% C.L. The exact C.L. depends somewhat on the choice of priors, and we discuss the effect of different priors as well as additional cosmological data.

In general correlated models, in addition to the usual adiabatic component with a spectral index n ad1 there is another adiabatic component with a spectral index n ad2 generated by entropy perturbation during inflation. We extend the analysis of a correlated mixture of adiabatic and isocurvature CMB fluctuations of the wmap group, who set the two adiabatic spectral indices equal. Allowing n ad1 and n ad2 to vary independently we find that the wmap data favor models where the two adiabatic components have opposite spectral tilts. Using the wmap data only, the 2σ upper bound for the isocurvature fraction fiso of the initial power spectrum at k0 = 0.05 Mpc −1 increases somewhat, e.g., from 0.76 of n ad2 = n ad1 models to 0.84 with a prior niso < 1.84 for the isocurvature spectral index. We also comment on a possible degeneration between the correlation component and the optical depth τ . Moreover, the measured low quadrupole in the TT angular power could be achieved by a strong negative correlation, but then one needs a large τ to fit the TE spectrum. Introduction. The first studies of mixed initial conditions for density perturbations in the light of measured cosmic microwave background (CMB) angular power assumed the adiabatic and isocurvature components to be uncorrelated [1,2,3]. About the same time it was pointed out that inflation with more than one scalar field may lead to a correlation between the adiabatic and isocurvature perturbations [4]. If the trajectory in the field space is curved during inflation, the entropy perturbation generates an adiabatic perturbation that is fully correlated with the entropy perturbation [5,6,7,8]. In addition, there is also the usual adiabatic perturbation created, e.g., by inflaton fluctuations. Thus, in the final angular power spectrum, one could have four different components: (1) the usual independent adiabatic component, (2) a second adiabatic component generated by the entropy perturbation during inflation, (3) an isocurvature component, and (4) a correlation between the second adiabatic and the isocurvature component. In this Letter we assume power laws for the initial power spectra of these components and denote their spectral indices by n ad1 , n ad2 , n iso , and n cor , respectively. Only three of these are free parameters, since, e.g., n cor = (n ad2 + n iso )/2.Although pure isocurvature models have been ruled out [9] after the clear detection of the second acoustic peak [10], the correlated mixture of adiabatic and isocurvature fluctuations still remains as an interesting possibility. In [7,11] angular power spectra have been calculated for correlated models and compared to the CMB data, but the spectral indices have either been fixed or set equal, n ad1 = n ad2 = n iso = n cor . This is not necessarily well motivated theoretically. For example, if the entropy field is slightly massive during inflation, then n ad1 < ∼ 1.0 < n iso in most models.Recently, the Wilkinson Microwave Anisotropy Probe (wmap) accurately measured the temperature anisotropy spectrum up ...