PEAKS IN THE COSMIC MICROWAVE BACKGROUND - FLAT VERSUS OPEN MODELS

We present properties of the peaks (maxima) of the microwave backgroun d anisotropies expected in hat and open cold dark matter models. We ob tain analytical expressions of several topological descriptors: mean n umber of maxima and the probability distribution of the Gaussian curva ture and the eccentricity of the peaks. These quantities are calculate d as functions of the radiation power spectrum, assuming a Gaussian di stribution of temperature anisotropies. We present results for angular resolutions ranging from 5' to 20' (antenna FWHM), scales that are re levant for the MAP and COBRAS/SAMBA space missions and the ground-base d interferometer experiments. Our analysis also includes the effects o f noise. We find that the number of peaks can discriminate between sta ndard cold dark matter models and that the Gaussian curvature distribu tion provides a useful test for these various models, whereas the ecce ntricity distribution cannot distinguish between them.