Xc. Luo, STATISTICAL TESTS FOR THE GAUSSIAN NATURE OF PRIMORDIAL FLUCTUATIONS THROUGH CBR EXPERIMENTS, Physical review. D. Particles and fields, 49(8), 1994, pp. 3810-3829
Information about the physical processes that generate the primordial
fluctuations in the early Universe can be gained by testing the Gaussi
an nature of the fluctuations through cosmic microwave background radi
ation (CBR) temperature anisotropy experiments. One of the crucial asp
ects of density perturbations that are produced by the standard inflat
ion scenario is that they are Gaussian, whereas seeds produced by topo
logical defects left over from an early cosmic phase transition tend t
o be non-Gaussian. To carry out this test, sophisticated statistical t
ools are required. In this paper, we will discuss several such statist
ical tools, including multivariant skewness and kurtosis, Euler-Poinca
re characteristics, the three-point temperature correlation function,
and Hotelling's T2 statistic defined through bispectral estimates of a
one-dimensional data set. The effect of noise present in the current
data is discussed in detail and the COBE 53 GHz data set is analyzed.
Our analysis shows that, on the large angular scale to which COBE is s
ensitive, the statistics are probably Gaussian. On the small angular s
cales, the importance of Hotelling's T2 statistic is stressed, and the
minimum sample size required to test Gaussianity is estimated. Althou
gh the current data set available from various experiments at half-deg
ree scales is still too small, improvement of the data set by roughly
a factor of 2 will be enough to test the Gaussianity statistically. On
the arc min scale, we analyze the recent RING data through bispectral
analysis, and the result indicates possible deviation from Gaussianit
y. Effects of point sources are also discussed. It is pointed out that
the Gaussianity problem can be resolved in the near future by ground-
based or balloon-borne experiments.