Primordial isocurvature perturbations: Testing the adiabaticity of the CMB anisotropy

Prospects for testing the adiabaticity of the primordial cosmological perturbations using MAP and PLANCK are evaluated. The most general cosmological perturbation in a universe with just baryons, photons, neutrinos, and a cold dark matter (CDM) component is described. In addition to the familiar adiabatic mode, there are four nonsingular isocurvature modes: a baryon isocurvature mode, a CDM isocurvature mode, a neutrino density isocurvature mode, and a neutrino velocity isocurvature mode. The most general perturbation is described by a $5×5,$ positive-definite, symmetric, matrix-valued function of wave number whose off-diagonal elements represent the correlations between the above mentioned modes. We found that when three modes and their correlations are admitted, the fractional uncertainties in the cosmological parameters and amplitudes of the isocurvature modes and their correlations become of order unity. These degeneracies, however, can be broken with the polarization information provided by PLANCK, reducing the uncertainties to below the ten percent level. Polarization is thus crucial to testing the adiabaticity of the primordial fluctuations.