Non-Gaussian Fluctuations

Abstract

Natural primordial mass density fluctuations are those for which the probability distribution, for the mass density fluctuations averaged over the horizon volume, is independent of time. This criterion determines the two-point correlation of the mass density fluctuations to have a Zeldovich power spectrum but allows for many types of higher correlations. If the connected higher correlations vanish the primordial fluctuations are Gaussian. In this case the probability distribution develops into a non-Gaussian one due to the non-linear time evolution. The nature of this non- Gaussian distribution and its effects on the large scale distribution of galaxies or clusters of galaxies and their large scale streaming velocities is explored. Next the possibility of natural primordial non-Gaussian fluctuations is examined. These can give rise to a very different large scale distribution of galaxies (or clusters of galaxies) than the Gaussian primordial fluctuations.