Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Non-linearity and Redshift-Space Distortion Effects

TL;DR

This paper investigates how nonlinear effects and redshift-space distortions influence the measurement of the baryon acoustic oscillation (BAO) scale, providing predictions and insights crucial for cosmological data analysis.

Contribution

It offers a perturbation theory-based analysis of BAO scale shifts due to nonlinearity and distortions, highlighting the importance of scale definition in data interpretation.

Findings

BAO scale shifts are less than 1% in real space for certain definitions.

Perturbation theory accurately predicts BAO shifts within its reliable scales.

The choice of BAO scale definition significantly affects the observed shifts.

Abstract

An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\lesssim$ 1%) relative to the prediction in {\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.