High-precision predictions for the acoustic scale in the non-linear regime

TL;DR

This paper achieves high-precision measurement of acoustic scale shifts caused by nonlinear effects in large-scale structure, using extensive simulations and various reconstruction techniques to improve accuracy and understand underlying physics.

Contribution

It provides a detailed analysis of nonlinear shifts in the acoustic scale, compares simulation results, and evaluates reconstruction methods, including 2LPT and iterative approaches.

Findings

Shift alpha(z) -1 = (0.300±0.015)% [D(z)/D(0)]^2 derived from simulations.

Density-field reconstruction reduces errors and restores correlations.

Propagator and mode-coupling terms help interpret nonlinear effects and estimate measurement signal-to-noise.

Abstract

We measure shifts of the acoustic scale due to nonlinear growth and redshift distortions to a high precision using a very large volume of high-force-resolution simulations. We compare results from various sets of simulations that differ in their force, volume, and mass resolution. We find a consistency within 1.5-sigma for shift values from different simulations and derive shift alpha(z) -1 = (0.300\pm 0.015)% [D(z)/D(0)]^{2} using our fiducial set. We find a strong correlation with a non-unity slope between shifts in real space and in redshift space and a weak correlation between the initial redshift and low redshift. Density-field reconstruction not only removes the mean shifts and reduces errors on the mean, but also tightens the correlations: after reconstruction, we recover a slope of near unity for the correlation between the real and redshift space and restore a strong correlation between the low and the initial redshifts. We derive propagators and mode-coupling terms from our N-body simulations and compared with Zeldovich approximation and the shifts measured from the chi^2 fitting, respectively. We interpret the propagator and the mode-coupling term of a nonlinear density field in the context of an average and a dispersion of its complex Fourier coefficients relative to those of the linear density field; from these two terms, we derive a signal-to-noise ratio of the acoustic peak measurement. We attempt to improve our reconstruction method by implementing 2LPT and iterative operations: we obtain little improvement. The Fisher matrix estimates of uncertainty in the acoustic scale is tested using 5000 (Gpc/h)^3 of cosmological PM simulations from Takahashi et al. (2009). (abridged)