We investigate the constraints imposed by the first-year WMAP CMB data extended to higher multipole by data from ACBAR, BOOMERANG, CBI and the VSA and by the LSS data from the 2dF galaxy redshift survey on the possible amplitude of primordial isocurvature modes. A flat universe with CDM and Lambda is assumed, and the baryon, CDM (CI), and neutrino density (NID) and velocity (NIV) isocurvature modes are considered. Constraints on the allowed isocurvature contributions are established from the data for various combinations of the adiabatic mode and one, two, and three isocurvature modes, with intermode cross-correlations allowed. Since baryon and CDM isocurvature are observationally virtually indistinguishable, these modes are not considered separately. We find that when just a single isocurvature mode is added, the present data allows an isocurvature fraction as large as 13+-6, 7+-4, and 13+-7 percent for adiabatic plus the CI, NID, and NIV modes, respectively. When two isocurvature modes plus the adiabatic mode and cross-correlations are allowed, these percentages rise to 47+-16, 34+-12, and 44+-12 for the combinations CI+NID, CI+NIV, and NID+NIV, respectively. Finally, when all three isocurvature modes and cross-correlations are allowed, the admissible isocurvature fraction rises to 57+-9 per cent. The sensitivity of the results to the choice of prior probability distribution is examined.
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