KURTOSIS, SKEWNESS, AND NON-GAUSSIAN COSMOLOGICAL DENSITY PERTURBATIONS

Cosmological topological defects as well as some nonstandard inflation models can give rise to non-Gaussian density perturbations. Skewness and kurtosis are the third and fourth moments that measure the deviati on of a distribution from a Gaussian. Measurement of these moments for the cosmological density field and for the microwave background tempe rature anisotropy can provide a test of the Gaussian nature of the pri mordial fluctuation spectrum. In the case of the density field, the im portance of measuring the kurtosis is stressed since it will be preser ved through the weakly nonlinear gravitational evolution epoch. Curren t constraints on skewness and kurtosis of primeval perturbations are o btained from the observed density contrast deltarho/rho on small scale s and from recent COBE observations of temperature anisotropies on lar ge scales. It is also shown how, in principle, future microwave anisot ropy experiments might be able to reveal the initial skewness and kurt osis. It is shown that present data argue that if the initial spectrum is adiabatic, then it is probably Gaussian, but non-Gaussian isocurva ture fluctuations are still allowed, and these are what topological de fects provide.