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

Abstract

We study the non-linear behavior of the baryon acoustic oscillation in the power spectrum and the correlation functionby decomposing the dark matter perturbations into the short- and long-wavelength modes.The evolution of the dark matter fluctuations can be described as aglobal coordinate transformation caused by the long-wavelength displacement vector acting on short-wavelengthmatter 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 ofthe 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 ofsimple and intuitive parts: the non-linear evolution of the smoothed power spectrum without the baryon acoustic oscillationsand the non-linear evolution of the baryon acoustic oscillationsdue 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 ∼ 7.7Mpc/hand describes the small non-linear shift in the peak position due to the galaxy random motions.