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The moments $T^2$, $T^3$, and $T^4$ of the cosmic microwave background (CMB) temperature fluctuations provide a test of the Gaussian nature of the initial density perturbations. The presence of instrumental noise in a CMB map biases these quantities in a fashion dependent on both the noise properties and the unknown CMB temperature field. We present analytic expressions for the biases and use Monte Carlo simulations to assess the best strategy for determining cosmologically interesting information from noisy data. The DMR data are consistent with a Gaussian power-law model of initial density perturbations. We fit the rms temperature variations $< T^2 >^{0.5}$ at various smoothing angles to derive the quadrupole normalization $Q_{rms-PS}$ and the power-law spectral index $n$.
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). The COBE program is supported by the Astrophysics Division of NASA's Office of Space Science and Applications.
