Lagrangian space consistency relation for large scale structure

TL;DR

This paper presents a Lagrangian space consistency relation for large scale structure, showing that certain squeezed correlation functions vanish, which could simplify understanding nonlinear regimes.

Contribution

It recasts existing consistency relations into a simple Lagrangian space statement, enhancing the potential for analytic insights into nonlinear large scale structure.

Findings

Squeezed correlation functions vanish in Lagrangian space.

Relation holds regardless of timing or multiple-streaming.

Simplifies the understanding of nonlinear large scale structure.

Abstract

Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present. The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.