Naonori S. Sugiyama, David N. Spergel
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 modes undergoing non-linear growth. This description clarifies the relation between the existing modified perturbation theories: the regularized multi-point propagator method, the Lagrangian resummation theory, and the standard perturbation theory. The regularized multi-point propagator method and the Lagrangian resummation theory partially include the non-linear effects from the global coordinate transformation. This implies that these two models do not have more effective information on the non-linear evolution of dark matter power spectrum than the standard perturbation theory, as the global coordinate transformation cancels due to the translation symmetry in the ensemble average. Our representations clarifies the success of the standard perturbation theory at the 2-loop level corrections in describing the amplitude of the non-linear power spectrum. 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. 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.
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http://arxiv.org/abs/1306.6660
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