The nonlinear probability distribution function in models with local primordial non-Gaussianity

We use the spherical evolution approximation to investigate nonlinear evolution from the non-Gaussian initial conditions characteristic of the local fnl model. We provide an analytic formula for the nonlinearly evolved probability distribution function of the dark matter which shows that the underdense tail of the nonlinear PDF in the fnl model should differ significantly from that for Gaussian initial conditions. Measurements of the underdense tail in numerical simulations may be affected by discreteness effects, and we use a Poisson counting model to describe this effect. Once this has been accounted for, our model is in good quantitative agreement with the simulations.