Time Non-locality in Dark Matter and LSS

TL;DR

This work demonstrates that time non-locality in large-scale structure manifests differently depending on symmetry: removing $SO(3)$ in favor of $SO(2)$ along the line of sight exposes time-nonlocal effects at third order in dark matter and bias operators, while the EFTofLSS stress tensor reveals non-locality at the same order. The authors show that the convective-derivative $Π$ basis efficiently captures non-local structures and provides an invertible mapping to the non-local basis, reducing the operator-count explosion at higher orders. They also show that selection (LoS) operators introduce non-locality at lower order, with direct implications for Lyman-$\alpha$ flux and redshift-space observations, including one-loop power spectra and renormalization considerations. Collectively, the results highlight the observable-dependent onset of time non-locality and offer practical computational tools for incorporating it in LSS analyses.

Abstract

We explore the intriguing phenomenon of time non-locality in the evolution of dark matter and Large Scale Structure (LSS). Recently in\,\cite{Donath:2023sav}, it was shown that time non-locality emerges in bias tracer fluctuations, which are $SO(3)$ scalars in real space, at fifth order in the perturbation expansion in dark matter overdensity. We demonstrate that by breaking the symmetry down to $SO(2)$, which is the case whenever line-of-sight effects become important, such as for flux fluctuations in the Lyman $α$ forest, the temporal non-locality appears at the third order in expansion. Additionally, within the framework of EFTofLSS, we demonstrate that time non-locality manifests in the effective stress tensor of dark matter, which is a second rank tensor under $SO(3)$ transformations, again at the third order in dark matter overdensity. Furthermore, we highlight the effectiveness of the standard $Π$ basis\,\cite{Mirbabayi:2014zca} in handling time non-local operators.