STATISTICAL TESTS FOR THE GAUSSIAN NATURE OF PRIMORDIAL FLUCTUATIONS THROUGH CBR EXPERIMENTS

Authors
Citation
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
Citations number
103
Categorie Soggetti
Physics, Particles & Fields
ISSN journal
05562821
Volume
49
Issue
8
Year of publication
1994
Pages
3810 - 3829
Database
ISI
SICI code
0556-2821(1994)49:8<3810:STFTGN>2.0.ZU;2-U
Abstract
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.