Gaussian Statistics of the Cosmic Microwave Background: Correlation of Temperature Extrema In the COBE DMR Two-Year Sky Maps

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 $a_{\mathrm{\ell }m}$ 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.