Determining cosmic microwave background structure from its peak distribution

We present a new method for time-efficient and accurate extraction of the p ower spectrum from future cosmic microwave background (CMB) maps based on p roperties of peaks and troughs of the Gaussian CMB sky. We construct a stat istic describing their angular clustering analogously to galaxies, the two- point angular correlation function xi (nu)(theta). We show that for increas ing peak threshold nu, xi (nu)(theta) is strongly amplified and becomes mea surable for nu greater than or similar to 1 on angular scales less than or equal to 10 degrees. Its amplitude at every scale depends uniquely on the C MB temperature correlation function, C(theta), and thus the measured xi (nu ) can be uniquely inverted to obtain C(theta) and its Legendre transform, t he power spectrum of the CMB field. Because in this method the CMB power sp ectrum is deduced from high peaks/troughs of the CMB field, the procedure t akes only [f(nu)]N-2(2) operations, where f(nu) is the fraction of pixels w ith \deltaT\ greater than or equal to nu standard deviations in the map of N pixels and is, e.g., 0.045 and 0.01 for nu = 2 and 2.5, respectively. We develop theoretical formalism for the method and show with detailed simulat ions, using the Microwave Anisotropy Probe mission parameters, that this me thod allows us to determine very accurately the CMB power spectrum from the upcoming CMB maps in only similar to (10(-4) to 10(-3)) N-2 operations.