Linear response to long wavelength fluctuations using curvature simulations

TL;DR

This paper investigates how long wavelength fluctuations affect cosmological structures using curvature simulations, providing a more precise method to measure halo biases and analyzing their impact on cosmological parameter estimation.

Contribution

It introduces a curvature simulation approach to study long wavelength effects, offering improved bias measurements and insights into super-sample variance and non-Gaussianity.

Findings

Bias measurements agree within a few percent between methods.

The response to variance differs from naive predictions by 18%.

Derived second order halo bias and super-sample variance contributions.

Abstract

We study the local response to long wavelength fluctuations in cosmological $N$-body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, most probably more precise, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the response of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naive derivation assuming a universal mass function by 18%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.