Modeling Nonlinear Evolution of Baryon Acoustic Oscillations: Convergence Regime of N-body Simulations and Analytic Models

TL;DR

The study quantifies nonlinear BAO evolution by comparing real-space matter power spectra from ΛCDM N-body simulations with three analytic models (SPT, RPT, CLA) while correcting finite-volume effects. It defines convergence wavenumbers $k^{\rm lim}_{1\%}$ and $k^{\rm lim}_{3\%}$ and provides an empirical rule for the convergence regime, showing RPT/CLA outperform SPT in the mildly nonlinear range and BAO phases remain robust beyond the amplitude regime. The authors demonstrate that with modes in the convergence regime, BAO scales can be recovered to about $1\%$ precision for upcoming surveys (e.g., WFMOS) at redshifts $z\sim1$–$3$, and they provide guidance on survey design and theoretical modeling, plus thorough tests of initialization, solvers, and box-size effects. The results guide interpretation of future BAO measurements, emphasize the importance of finite-volume corrections and higher-order perturbation theory, and point to extensions to redshift space and velocity fields for full cosmological constraints.

Abstract

We use a series of cosmological N-body simulations and various analytic models to study the evolution of the matter power spectrum in real space in a ΛCold Dark Matter universe. We compare the results of N-body simulations against three analytical model predictions; standard perturbation theory, renormalized perturbation theory, and the closure approximation. We include the effects from finite simulation box size in the comparison. We determine the values of the maximum wavenumbers, k^{lim}_{1%} and k^{lim}_{3%}, below which the analytic models and the simulation results agree to within 1 and 3 percent, respectively. We then provide a simple empirical function which describes the convergence regime determined by comparison between our simulations and the analytical models. We find that if we use the Fourier modes within the convergence regime alone, the characteristic scale of baryon acoustic oscillations can be determined within 1% accuracy from future surveys with a volume of a few h^{-3}Gpc^3 at z\sim1 or z\sim3 in the absence of any systematic distortion of the power spectrum.

Figures (10)

• Figure 1: A flow chart to illustrate our methodology to correct for the effect of finite box size.
• Figure 2: Comparison of simulation power spectra and analytical predictions: Left: Power spectra of our simulations before correction, normalized by the no-wiggles formula; top$z=3$, middle$z=1$, bottom$z=0$. The errorbars show the standard errors [equation (\ref{['eq:error1']})]. Lines are theoretical predictions described in section \ref{['sec:nonlinear']}; dotted: standard perturbation theory (SPT), dot-dashed: renormalized perturbation theory (RPT), dashed: closure approximation (CLA), solid: linear theory (LIN). Right: Same as the left panel but we plot the difference from the RPT prediction.
• Figure 3: Same as figure \ref{['fig:raw']}, but we correct for the effect of finite volume. We truncate the expansion of equation (\ref{['eq:deltaPT']}) at the first term. The errorbars show equation (\ref{['eq:error3']}).
• Figure 4: Same as figure \ref{['fig:raw']}, but we correct for the effect of finite volume including the second term of equation (\ref{['eq:deltaPT']}). We also show the $1\%$ limit wavenumbers, $k_{1\%}^{\rm lim}$, for LIN, SPT and RPT/CLA by vertical arrows (from left to right).
• Figure 5: Upper limit of reliable wavenumbers, $k_{1\%}^{\rm lim}$ and $k_{3\%}^{\rm lim}$, described in the text. Symbols show the values read from figure \ref{['fig:ICV+FMC']}. circles: linear theory, triangles: SPT, squares: RPT/CLA. Filled symbols correspond to $k^{\rm lim}_{1\%}$, while open ones represent $k^{\rm lim}_{3\%}$. The three solid lines plot equation (\ref{['eq:validk']}): $k_{1\%}^{\rm lim}$ for linear theory ($C=0.06$), SPT ($C=0.18$) and RPT/CLA ($C=0.35$) from left to right, and the dashed lines are corresponding $k_{3\%}^{\rm lim}$ ($C=0.13$, $0.3$ and $0.5$, respectively). We also show the nonlinear wavenumbers proposed by Jeong2006, Sefusatti2007 and Matsubara2008 as dotted lines with JK06, SK07 and M08. The two shaded regions show the redshift range planed by WFMOS survey (with minimum wavenumbers, $2\pi/V^{1/3}$. Here $V$ is the survey volume.).