Accurate predictions from small boxes: variance suppression via the Zel'dovich approximation

TL;DR

This paper presents a method combining Lagrangian perturbation theory with N-body simulations using Zel'dovich displacements as control variates, significantly reducing variance in large-scale structure predictions and enabling more accurate emulators and measurements in limited-volume simulations.

Contribution

It introduces a novel variance reduction technique using Zel'dovich displacements to improve the accuracy of simulation-based predictions in cosmology.

Findings

Achieves hundredfold reduction in sample variance.

Extends matter and tracer field emulators to larger scales.

Enhances measurement accuracy in small-volume simulations.

Abstract

Simulations have become an indispensable tool for accurate modelling of observables measured in galaxy surveys, but can be expensive if very large dynamic range in scale is required. We describe how to combine Lagrangian perturbation theory models with N-body simulations to reduce the effects of finite computational volume in the prediction of ensemble average properties in the simulations within the context of control variates. In particular we use the fact that Zel'dovich displacements, computed during initial condition generation for any simulation, correlate strongly with the final density field. Since all the correlators of biased tracers can be computed with arbitrary precision for these displacements, pairing the Zel'dovich `simulation' with the N-body realization allows hundredfold reductions in sample variance for power spectrum or correlation function estimation. Zel'dovich control variates can accurately extend matter or tracer field emulators to larger scales than previously possible, as well as improving measurements of statistics in simulations which are inherently limited to small volumes, such as hydrodynamical simulations of galaxy formation and reionization.