Peaks in the Cosmic Microwave Background: Flat versus Open Models

We present properties of the peaks (maxima) of the microwave background anisotropies expected in flat and open cold dark matter models. We obtain analytical expressions of several topological descriptors: mean number of maxima and the probability distribution of the Gaussian curvature and the eccentricity of the peaks. These quantities are calculated as functions of the radiation power spectrum, assuming a Gaussian distribution of temperature anisotropies. We present results for angular resolutions ranging from 5' to 20' (antenna FWHM), scales that are relevant for the MAP and COBRAS/SAMBA space missions and the ground-based interferometer experiments. Our analysis also includes the effects of noise. We find that the number of peaks can discriminate between standard cold dark matter models and that the Gaussian curvature distribution provides a useful test for these various models, whereas the eccentricity distribution cannot distinguish between them.