The Shift of the Baryon Acoustic Oscillation Scale: A Simple Physical Picture

TL;DR

This paper explains the physical reasons behind the observed shift of the BAO scale to smaller values in simulations, emphasizing the role of overdense regions and providing analytic expressions that align with simulation results.

Contribution

It offers a simple physical picture and analytic formulas for the non-linear BAO scale shift, clarifying the effects of overdensities and bias, and supports the effectiveness of reconstruction methods.

Findings

The BAO scale shift is mainly due to overdense regions acting as positively curved universes.

Analytic expressions accurately predict the non-linear shift observed in simulations.

Reconstruction methods can effectively reverse the BAO scale shift.

Abstract

A shift of the baryon acoustic oscillation (BAO) scale to smaller values than predicted by linear theory was observed in simulations. In this paper, we try to provide an intuitive physical understanding of why this shift occurs, explaining in more pedagogical detail earlier perturbation theory calculations. We find that the shift is mainly due to the following physical effect. A measurement of the BAO scale is more sensitive to regions with long wavelength overdensities than underdensities, because (due to non-linear growth and bias) these overdense regions contain larger fluctuations and more tracers and hence contribute more to the total correlation function. In overdense regions the BAO scale shrinks because such regions locally behave as positively curved closed universes, and hence a smaller scale than predicted by linear theory is measured in the total correlation function. Other effects which also contribute to the shift are briefly discussed. We provide approximate analytic expressions for the non-linear shift including a brief discussion of biased tracers and explain why reconstruction should entirely reverse the shift. Our expressions and findings are in agreement with simulation results, and confirm that non-linear shifts should not be problematic for next-generation BAO measurements.