Non-local-in-time structure formation and sixth-order galaxy bias
Alex Edison, Matthew Lewandowski, Leonardo Senatore
TL;DR
The paper develops a comprehensive non-local-in-time bias framework for galaxies within the EFT of Large-Scale Structure, deriving a complete sixth-order expansion. It introduces a time-nonlocal construction based on fluid trajectories and NRNGP diffeomorphisms, yielding $57$ independent bias operators at sixth order (versus $46$ locally) and establishing recursion relations for perturbative kernels plus explicit multi-leg soft-limit identities. The work demonstrates that higher-order clustering statistics can distinguish local- vs non-local-in-time galaxy formation at fixed redshift and provides explicit procedures for both real-space and Fourier-space kernel limits up to $n=6$. These results lay the groundwork for more precise modeling of galaxy bias, including potential extensions to higher-derivative terms and stochastic contributions.
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.