The correlation of peaks in the microwave background

We present accurate small-angle predictions of the correlation function of hotspots in the microwave background radiation for Gaussian theories such a s those predicted in most inflation models. The correlation function of pea ks above a certain threshold depends only on the threshold and the power sp ectrum of temperature fluctuations. Since these are both potentially observ able quantities in a microwave background map, there are no adjustable para meters in the predictions. These correlations should therefore provide a po werful test of the Gaussian hypothesis, and provide a useful discriminant b etween inflation and topological defect models such as the cosmic string mo del. The correlations have a number of oscillatory features, which should b e detectable at high signal-to-noise ratio with future satellite experiment s such as MAP and Planck.