Consistency relations for large scale structures with primordial non-Gaussianities

TL;DR

This paper explores how primordial non-Gaussianities alter the fundamental consistency relations in large-scale structure formation, providing conditions under which these relations revert to their Gaussian form.

Contribution

It derives modified consistency relations accounting for non-Gaussian initial conditions and identifies conditions for their Gaussian limit, extending previous Gaussian-based frameworks.

Findings

Modified consistency relations include all-order mixed correlations.

Conditions identified for the relations to reduce to Gaussian form.

Results applicable to biased tracers and velocity/momentum correlations.

Abstract

We investigate how the consistency relations of large-scale structures are modified when the initial density field is not Gaussian. We consider both scenarios where the primordial density field can be written as a nonlinear functional of a Gaussian field and more general scenarios where the probability distribution of the primordial density field can be expanded around the Gaussian distribution, up to all orders over $\delta_{L0}$. Working at linear order over the non-Gaussianity parameters $f_{\rm NL}^{(n)}$ or $S_n$, we find that the consistency relations for the matter density fields are modified as they include additional contributions that involve all-order mixed linear-nonlinear correlations $\langle \prod \delta_L \prod \delta \rangle$. We derive the conditions needed to recover the simple Gaussian form of the consistency relations. This corresponds to scenarios that become Gaussian in the squeezed limit. Our results also apply to biased tracers, and velocity or momentum cross-correlations.