Dimensionality

Limits on the anisotropy of the microwave background provide strong constraints on theories of galaxy formation which incorporate non-baryonic dark matter. We focus on scale-invariant perturbations, which may be in either an adiabatic or an isocurvature mode. Adiabatic models with cold dark matter in which galaxies trace the mass distribution lead to excessive small-scale anisotropies unless $\Omega _{0}$ h$_{0}^{\frac{2}{3}}$ > 0.2. This apparently conflicts with the low value of $\Omega _{0}$ deduced from dynamical studies of galaxy clustering. This difficulty may be resolved if galaxies are biased tracers of the mass. Isocurvature cold dark-matter models are incompatible with observations even if $\Omega _{0}$ = 1 unless the amplitude of the galaxy correlation function is more than four times that of the mass distribution. The statistics of the radiation pattern may provide a useful test of the Gaussian nature of the fluctuations.