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The angular distribution of the cosmic microwave background (CMB) probes the distribution of mass and energy in the early universe and provides a means to test competing models of structure formation. One such test is whether or not the distribution of CMB anisotropies follows Gaussian statistics. Attempts to differentiate Gaussian from non-Gaussian distributions on large angular scales are complicated by the tendency of any distribution to approach Gaussian when averaged over a sufficiently large area (the central limit theorem) and by our inability to measure more than one sample (our observable universe) of the theoretical parent distribution (``cosmic variance''). We use the two-point correlation function of the extrema points (peaks and valleys) in the COBE Differential Microwave Radiometers (DMR) 2-year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum likelihood analysis compares the DMR data to $n=1$ toy models whose random-phase spherical harmonic components $a_{\ell m}$ are drawn from either Gaussian, $\chi^2$, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. All non-Gaussian models tested are ruled out at 90\% confidence, limited by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.
The National Aeronautics and Space Administration/Goddard Space Flight Center (NASA/GSFC) is responsible for the design, development, and operation of the Cosmic Background Explorer (COBE ). Scientific guidance is provided by the COBE Science Working Group.
