Nonlinear Structure Formation and the Acoustic Scale

We present high signal-to-noise ratio measurements of the acoustic scale in the presence of nonlinear growth and redshift distortions using 320 h⁻³ Gpc ³ of cosmological particle-mesh simulations. Using simple fitting methods, we obtain robust measurements of the acoustic scale with scatter close to that predicted by the Fisher matrix. We detect and quantify the shift in the acoustic scale by analyzing the power spectrum: we detect at greater than 5 σ a decrease in the acoustic scale in the real-space matter power spectrum of 0.2% at z = 1.5, growing to 0.45% at z = 0.3. In redshift space, the shifts are about 25% larger: we detect a decrease of 0.25% at z = 1.5 and 0.54% at z = 0.3. Despite the nonzero amounts, these shifts are highly predictable numerically, and hence removable within the standard ruler analysis of clustering data. Moreover, we show that a simple density field reconstruction method substantially reduces the scatter and nonlinear shifts of the acoustic scale measurements: the shifts are reduced to less than 0.1% at z = 0.3–1.5, even in the presence of nonnegligible shot noise. Finally, we show that the ratio of the cosmological distance to the sound horizon that would be inferred from these fits is robust to variations in the parameterization of the fitting method and reasonable differences in the template cosmology.