How does non-linear dynamics affect the baryon acoustic oscillation?

TL;DR

This paper investigates how non-linear dynamics influence baryon acoustic oscillations by decomposing dark matter perturbations, revealing the effectiveness of standard perturbation theory and proposing an improved model for better accuracy.

Contribution

It introduces an extension to the 2-loop perturbation theory that more accurately models non-linear BAO evolution, accounting for large-scale velocity effects and peak smoothing.

Findings

Standard perturbation theory's cancellation of high-k solutions explains its success.

The extended model predicts BAO peak smoothing of ~7.7 Mpc/h at z=0.35.

The model captures small non-linear shifts in the BAO peak position.

Abstract

We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation function by decomposing the dark matter perturbations into the short- and long-wavelength modes. The evolution of the dark matter fluctuations can be described as a global coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelength matter perturbation undergoing non-linear growth. Using this feature, we investigate the well known cancellation of the high-$k$ solutions in the standard perturbation theory. While the standard perturbation theory naturally satisfies the cancellation of the high-$k$ solutions, some of the recently proposed improved perturbation theories do not guarantee the cancellation. We show that this cancellation clarifies the success of the standard perturbation theory at the 2-loop order in describing the amplitude of the non-linear power spectrum even at high-$k$ regions.We propose an extension of the standard 2-loop level perturbation theory model of the non-linear power spectrum that more accurately models the non-linear evolution of the baryon acoustic oscillation than the standard perturbation theory. The model consists of simple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillations and the non-linear evolution of the baryon acoustic oscillations due to the large-scale velocity of dark matter and due to the gravitational attraction between dark matter particles. Our extended model predicts the smoothing parameter of the baryon acoustic oscillation peak at $z=0.35$ as $\sim 7.7\ {\rm Mpc}/h$ and describes the small non-linear shift in the peak position due to the galaxy random motions.