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

TL;DR

This paper delivers high-precision predictions for the acoustic scale in the nonlinear regime by combining large-volume, high-resolution N-body simulations with a robust fitting and reconstruction pipeline. It quantifies how nonlinear growth and redshift distortions shift the BAO scale, decomposes the nonlinear power into a propagator and a mode-coupling term, and demonstrates that density-field reconstruction largely removes these shifts and improves the signal-to-noise of BAO measurements. The work validates the use of Fisher-matrix error estimates against extensive N-body results and shows only modest gains from 2LPT and iterative reconstruction. Overall, the acoustic scale can be predicted and recovered with sub-percent accuracy, enabling precise BAO-based cosmological inferences.

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)

Figures (13)

• Figure 1: Power spectra divided by a smooth, nowiggle power spectrum $P_{\rm nw}$ at z=3.0, 1.0, and 0.3 in real (left) and redshift space(right), before (black for G576 and red for G1024) and after reconstruction (blue for G576 and magenta for G1024). The dashed line is the linear theory model. The dotted line at $z=1$ is from the halofit model from Smith03. We do not subtract shot noise.
• Figure 2: The nonlinear evolution of shifts $\alpha-1$ with redshift. Top panels show the mean and the errors of the mean of $\alpha$ before reconstruction. The broken lines with the corresponding colors are the expected nonlinear shifts derived using the second order perturbation theory, as in Pad09. In the bottom panels, solid points show the values after reconstruction, in comparison to the values before reconstruction (open points). Data points for G1024 are slightly displaced in $z$ for clarification. We note that the sample variance is highly correlated between shifts at different redshifts for a given set of simulations. The solid red line in the bottom panel is our best fit to $\alpha(z)-1 \propto [D(z)/D(0)]^2$ when including the covariance between redshifts.
• Figure 3: $\alpha-1$ of 1000 subsamples from 63 boxes of G576 at $z=0.3$, before reconstruction (left) and after reconstruction (right). Each subsample is generated by a random resampling of $M=31$ boxes out of the total $N=63$ boxes without replacement. $\alpha_r-1$ denotes shift values in real space and $\alpha_s-1$ is for redshift space. The red error bars denote the mean and the standard deviation of $\alpha-1$. Note that the standard deviation among subsamples closely represents the scatter associated with the mean of $\alpha$ as $M \sim N/2$. The gray diagonal lines are graphical representation of the distribution of the differences in $\alpha$'s: the y-intercept or x-intercept of the middle gray line shows $\Delta \alpha$ and the outer gray lines depict a $1-\sigma$ range for $\Delta \alpha$.
• Figure 4: $\alpha-1$ for all the subsamples for G576 at $z=1.0$. The red error bars denote the mean and errors of $\alpha-1$.
• Figure 5: $\alpha-1$ for all the subsamples for G1024 at $z=1.0$ (black points) before reconstruction (left) and after reconstruction (right). The red error bars denote the mean and errors of $\alpha-1$. The standard deviations of the subsamples is equal to the scatter associated with the mean of $\alpha$. We superimpose the result of G576 at $z=1$ with a blue error bar, for comparison.