Non-local-in-time structure formation and sixth-order galaxy bias

TL;DR

This paper develops a comprehensive non-local-in-time galaxy bias expansion up to sixth order within the Effective Field Theory of Large-Scale Structure, revealing additional bias operators and implications for galaxy formation history.

Contribution

It introduces the complete sixth-order non-local-in-time bias operators, expanding the theoretical framework for galaxy clustering analysis.

Findings

Identifies 57 independent bias operators at sixth order, compared to 46 in local-in-time models.

Shows higher-order statistics can distinguish local versus non-local galaxy formation.

Derives recursion relations and soft limits for perturbative kernels.

Abstract

We present a systematic construction of the non-local-in-time galaxy bias expansion in the Effective Field Theory of Large-Scale Structure. In order to fully capture time non-locality up to sixth order, we must take into account that every field can contribute non-locally from a separate time in the past. Starting from the general non-local-in-time expression for the galaxy overdensity, we explicitly compute the complete sixth-order basis of bias operators at leading order in spatial derivatives, finding 57 independent biases, compared to 46 in the corresponding local-in-time expansion. As previously found at fifth order, this difference implies that higher-order clustering statistics can distinguish between local- and non-local-in-time galaxy formation, and thus are sensitive, at a single redshift, to the formation time of galaxies. Along the way, we obtain recursion relations for the perturbative kernels and show that they satisfy specific multi-leg soft limits when the sum of a subset of the external momenta goes to zero.