The Bispectrum in Lagrangian Perturbation Theory

TL;DR

This paper develops an efficient method to compute the bispectrum in Lagrangian perturbation theory, focusing on the Zeldovich approximation, and compares IR resummation techniques with implications for modeling cosmic features.

Contribution

It introduces a novel approach to calculate the bispectrum in LPT, especially the Zeldovich approximation, and compares IR resummation methods with applications to N-point functions.

Findings

LPT bispectrum computation is efficient and IR-safe.

IR resummation methods in LPT and EPT agree at 1-loop.

LPT better captures nonlinear damping without spectrum splitting.

Abstract

We study the bispectrum in Lagrangian perturbation theory. Extending past results for the power spectrum, we describe a method to efficiently compute the bispectrum in LPT, focusing on the Zeldovich approximation, in which contributions due to linear displacements are captured to all orders in a manifestly infrared (IR) safe way. We then isolate the effects of these linear displacements on oscillatory components of the power spectrum like baryon acoustic oscillations or inflationary primordial features and show that the Eulerian perturbation theory (EPT) prescription wherein their effects are resummed by a Gaussian damping of the oscillations arise as a saddle-point approximation of our calculation. These two methods of IR resummation are in excellent agreement at 1-loop in the bispectrum. At tree level, resummed EPT does less well to capture the nonlinear damping of the oscillations, and the LPT calculation does not require an artificial split of the power spectrum into smooth and oscillatory components, making the latter particularly useful for modeling exotic features. We finish by extending our analysis of IR resummation in LPT to N-point functions of arbitrary order.