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

TL;DR

This paper investigates how primordial non-Gaussianity affects the nonlinear evolution of the redshift space density field, revealing significant differences in the underdense tail compared to Gaussian models, and extends Kaiser's formula accordingly.

Contribution

It introduces a method to analyze the nonlinear redshift space PDF with local primordial non-Gaussianity using the ellipsoidal collapse approximation.

Findings

Underdense tail of the PDF differs significantly from Gaussian cases.

Derived the lowest order correction to Kaiser's formula for non-zero f_{nl}.

Showed the impact of primordial non-Gaussianity on redshift space distortions.

Abstract

We use the ellipsoidal collapse approximation to investigate the nonlinear redshift space evolution of the density field with primordial non-Gaussianity of the local f_{nl}-type. We utilize the joint distribution of eigenvalues of the initial non-Gaussian shear field and evaluate the evolved redshift space probability distribution function (PDF). It is shown that, similar to the real space analysis, the underdense tail of the nonlinear redshift space PDF differs significantly from that for Gaussian initial conditions. We also derive the lowest order correction of the Kaiser's formulain the presence of a non-zero f_{nl}.