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

TL;DR

This paper develops an analytic model for the nonlinear probability distribution function of dark matter in local primordial non-Gaussianity models, highlighting differences in under-dense regions and validating with simulations.

Contribution

It provides a new analytic formula for the nonlinear PDF in local f_nl models, accounting for discreteness effects and matching simulation results.

Findings

The nonlinear PDF's under-dense tail differs significantly from Gaussian cases.

Discreteness effects can bias measurements of the under-dense tail.

The analytic model agrees well with numerical simulations after corrections.

Abstract

We use the spherical evolution approximation to investigate nonlinear evolution from the non-Gaussian initial conditions characteristic of the local f_nl model. We provide an analytic formula for the nonlinearly evolved probability distribution function of the dark matter which shows that the under-dense tail of the nonlinear PDF in the f_nl model should differ significantly from that for Gaussian initial conditions. Measurements of the under-dense 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.