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

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 ongoing and/or future galaxy surveys aim to detect and precisely determine 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 for 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, ApJ, 657, 51) indeed shows very small shifts (≲ 1%) relative to the prediction in linear theory in real space. The shifts can be predicted accurately for scales where perturbation theory is reliable