Gauge invariant cosmological perturbations with cold dark matter

In the gauge-invariant formalism, the evolution of adiabatic and baryonic isocurvature density perturbations in a universe dominated by cold dark matter (CDM) is thoroughly investigated. We evaluate anisotropies in the cosmic microwave background (CMB) and large scale peculiar velocities. From the recent observations of CMB fluctuations, we find new and stringent constraint is obtained for adiabatic CDM models as Ω0 h-1 > 0.3. As for baryonic isocurvature perturbations, though the constraint is required as Ω0 h-1 >approx 0.6, we find these baryonic isocurvature models are more viable than axion isocurvature models. However it is difficult for both adiabatic and baryonic isocurvature CDM models to explain to observed large scale velocity field at >approx 50h-1 Mpc while being consistent with the observations of CMB anisotropies. (author)