Separate Universe Simulations

TL;DR

This paper introduces a method using separate universe simulations to accurately measure how large-scale density fluctuations influence small-scale observables in cosmology, enabling efficient and precise analysis.

Contribution

It derives a fully non-linear mapping for separate universe simulations and demonstrates their application to measure the response of the matter power spectrum to long-wavelength perturbations.

Findings

Percent-level precision in response measurements over various scales

Efficient technique applicable to diverse observables

Provides a detailed step-by-step simulation and analysis procedure

Abstract

The large-scale statistics of observables such as the galaxy density are chiefly determined by their dependence on the local coarse-grained matter density. This dependence can be measured directly and efficiently in N-body simulations by using the fact that a uniform density perturbation with respect to some fiducial background cosmology is equivalent to modifying the background and including curvature, i.e., by simulating a "separate universe". We derive this mapping to fully non-linear order, and provide a step-by-step description of how to perform and analyse the separate universe simulations. This technique can be applied to a wide range of observables. As an example, we calculate the response of the non-linear matter power spectrum to long-wavelength density perturbations, which corresponds to the angle-averaged squeezed limit of the matter bispectrum and higher $n$-point functions. Using only a modest simulation volume, we obtain results with percent-level precision over a wide range of scales.