Predictions of a non-Gaussian model for large scale structure

Abstract

A modified CDM model for the origin of structure in the universe based on an inflation model with two interacting scalar fields, is analyzed to make predictions for the statistical properties of the density and velocity fields and the microwave background anisotropy. The initial gauge-invariant potential {zeta} which is defined as {zeta} = {delta}{rho}/({rho} + p) + 3{var_phi}, where {var_phi} is the curvature perturbation amplitude and p is the pressure, is the sum of a Gaussian field {phi}{sub 1}, and the square of a Gaussian field {phi}{sub 2}. A Harrison-Zel`dovich scale-invariant power spectrum is assumed for {phi}{sub 1}; and a log-normal `peak` power spectrum for {phi}{sub 2}. The location and the width of the peak are described by parameters k{sub c} and a. respectively. The model is motivated to some extent by inflation models with two interacting scalar fields, but is mainly interesting as an example of a model whose statistical properties change with scale. On small scales, it is almost identical to a standard scale-invariant Gaussian CDM model. On scales near the location of the peak of the non-Gaussian field, the distributions have long tails in high positive values of the density and velocity fields. Thus, it is easier to get large-scale streaming velocities than the standard CDM model. The quadrupole amplitude of fluctuations of the cosmic microwave background radiation and the rms variation of the temperature field smoothed with a 10{degree} FWHM Gaussian are calculated; a reasonable agreement is found with the new COBE results.