The Abundance of High-Redshift Objects as a Probe of Non-Gaussian Initial Conditions

The observed abundance of high-redshift galaxies and clusters contains precious information about the properties of the initial perturbations. We present a method to compute analytically the number density of objects as a function of mass and redshift for a range of physically motivated non-Gaussian models. In these models the non-Gaussianity can be dialed from zero and is assumed to be small. We compute the probability density function for the smoothed dark matter density field, and we extend the Press-Schechter approach to mildly non-Gaussian density fields. The abundance of high-redshift objects can be directly related to the non-Gaussianity parameter and thus to the physical processes that generated deviations from the Gaussian behavior. Even a skewness parameter of order 0.1 implies a dramatic change in the predicted abundance of z>~1 objects. Observations from the Next Generation Space Telescope (NGST) and X-ray satellites (XMM) can be used to accurately measure the amount of non-Gaussianity in the primordial density field.