Multi-Point Propagators for Non-Gaussian Initial Conditions

TL;DR

This paper extends Renormalized Perturbation Theory to include primordial non-Gaussian initial conditions, demonstrating the preservation of the series reordering scheme and analyzing the properties of multi-point propagators in this context.

Contribution

It introduces a method to incorporate primordial non-Gaussianity into RPT calculations and investigates the properties of multi-point propagators under these conditions.

Findings

The series reordering scheme applies to non-Gaussian initial conditions.

Multi-point propagators are unchanged at one-loop order regardless of initial statistics.

High-momentum behavior of propagators can be explicitly computed for arbitrary initial conditions.

Abstract

We show here how Renormalized Perturbation Theory (RPT) calculations applied to the quasi-linear growth of the large-scale structure can be carried on in presence of primordial non-Gaussian (PNG) initial conditions. It is explicitly demonstrated that the series reordering scheme proposed in Bernardeau, Crocce and Scoccimarro (2008) is preserved for non-Gaussian initial conditions. This scheme applies to the power spectrum and higher order spectra and is based on a reorganization of the contributing terms into sum of products of multi-point propagators. In case of PNG new contributing terms appear, the importance of which is discussed in the context of current PNG models. The properties of the building blocks of such resummation schemes, the multi-point propagators, are then investigated. It is first remarked that their expressions are left unchanged at one-loop order irrespectively of statistical properties of the initial field. We furthermore show that the high-momemtum limit of each of these propagators can be explicitly computed even for arbitrary initial conditions. They are found to be damped by an exponential cutoff whose expression is directly related to the moment generating function of the one-dimensional displacement field. This extends what had been established for multi-point propagators for Gaussian initial conditions. Numerical forms of the cut-off are shown for the so-called local model of PNG.