Non-Gaussian Statistics at Large Angular Scales: {\it COBE} DMR 2-Year Sky Maps
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**Session 57 -- COBE and Related Papers**
*Display presentation, Tuesday, 10, 1995, 9:20am - 6:30pm*

## [57.02] Non-Gaussian Statistics at Large Angular Scales: {\it COBE} DMR 2-Year Sky Maps

*C.L. Bennett (NASA/GSFC), A. Kogut, G. Hinshaw (HSTX), A.J. Banday (USRA), P.M. Lubin (UCSB), G.F. Smoot (UCB)*
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.

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