On the Robustness of the Acoustic Scale in the Low‐Redshift Clustering of Matter

We discuss the effects of non-linear structure formation on the signature ofacoustic oscillations in the late-time galaxy distribution. We argue that thedominant non-linear effect is the differential motion of pairs of tracersseparated by 150 Mpc. These motions are driven by bulk flows and clusterformation and are much smaller than the acoustic scale itself. We present amodel for the non-linear evolution based on the distribution of pairwiseLagrangian displacements that provides a quantitative model for the degradationof the acoustic signature, even for biased tracers in redshift space. TheLagrangian displacement distribution can be calibrated with a significantlysmaller set of simulations than would be needed to construct a precise powerspectrum. By connecting the acoustic signature in the Fourier basis with thatin the configuration basis, we show that the acoustic signature is more robustthan the usual Fourier-space intuition would suggest because the beat frequencybetween the peaks and troughs of the acoustic oscillations is a very smallwavenumber that is well inside the linear regime. We argue that any possibleshift of the acoustic scale is related to infall on 150 Mpc scale, which isO(0.5%) fractionally at first-order even at z=0. For the matter, there is afirst-order cancellation such that the mean shift is O(10^{-4}). However,galaxy bias can circumvent this cancellation and produce a sub-percentsystematic bias.Comment: 27 pages, LaTeX. Submitted to the Astrophysical Journa