The most general homogeneous and isotropic statistical ensemble of linear scalar perturbations regular at early times in a universe with only photons, baryons, neutrinos, and a cold dark matter (CDM) component is described by a $5\times 5$ symmetric matrix-valued generalization of the power spectrum. This description is complete if the perturbations are Gaussian, and even in the non-Gaussian case determines the expectation values of all observables quadratic in the small perturbations. The matrix valued power spectrum describes the auto and cross correlations of the adiabatic, baryon isocurvature, CDM isocurvature, neutrino density isocurvature, and neutrino velocity isocurvature modes. In this paper we examine the prospects for constraining or discovering isocurvature modes using forthcoming MAP and Planck measurements of the cosmic microwave background (CMB) anisotropy. We also consider the degradation in estimates of the cosmological parameters resulting from the inclusion of these modes. In the case of the MAP measurement of the temperature alone, the degradation is catastrophic. When isocurvature modes are admitted, uncertainties in the amplitudes of the mode auto- and cross correlations, and in the cosmological parameters, become of order one. With the inclusion of polarization (at an optimistic sensitivity) the situation improves for the cosmological parameters, but the isocurvature modes are still only weakly constrained. Measurements with Planck’s estimated errors are far more constraining once polarization is included. If Planck operates as planned, the amplitudes of isocurvature modes will be constrained to less than 10% of the adiabatic mode, and simultaneously key cosmological parameters will be estimated to within a few percent or better.

• Received 20 December 2000

DOI:https://doi.org/10.1103/PhysRevD.66.023528