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

TL;DR

This study explains why nonlinear gravitational evolution shifts the BAO standard ruler to smaller scales. By separating long- and short-wavelength modes, the authors show that overdense regions contribute more to the measured correlation function, and that local curvature in these regions reduces the observed BAO scale; they formalize this with second-order Eulerian perturbation theory and include tracer bias, yielding analytic expressions for real- and Fourier-space shifts. The predicted shifts, $\alpha-1=131/105\langle\delta_L^2\rangle$ (real space) and $\alpha_k-1=47/105\langle\delta_L^2\rangle$ (Fourier space), align with simulations, and reconstruction via the Zel'dovich approach should reverse the shift. Overall, the sub-percent nonlinear BAO shift, and its reversibility, supports the robustness of BAO as a precise cosmological standard ruler for future surveys.

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.