Time Non-locality in Dark Matter and LSS

TL;DR

This paper investigates how time non-locality arises in dark matter and large-scale structure evolution, showing it appears at different orders depending on symmetry considerations and affecting the effective stress tensor.

Contribution

It demonstrates the emergence of time non-locality at third order in perturbation expansion under certain symmetry breakings and discusses its treatment within EFTofLSS.

Findings

Time non-locality appears at fifth order for bias tracer fluctuations with full SO(3) symmetry.

Breaking symmetry to SO(2) lowers the order to third for flux fluctuations in Lyman α forest.

Time non-locality manifests in the effective stress tensor at third order in dark matter overdensity.

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 $\alpha$ 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 $\Pi$ basis\,\cite{Mirbabayi:2014zca} in handling time non-local operators.