Reconstructing Baryon Oscillations: A Lagrangian Theory Perspective

TL;DR

This work addresses how to recover the linear BAO signal from nonlinear structure growth by analyzing Eisenstein et al.'s reconstruction within the Lagrangian perturbation theory framework. It shows that the reconstructed density is not exactly the linear density at second order, yet the procedure reduces nonlinear damping of the BAO feature by effectively lowering the damping scales, as evidenced by the decomposition P_recon = P_ss + P_dd - 2 P_sd with distinct dampings Σ_ss, Σ_sd, Σ_dd. In the LPT treatment, the leading mode-coupling term is suppressed through a modified kernel, explaining the reduced acoustic-scale shift and improved calibration. The natural smoothing scale R ≈ Σ minimizes higher-order corrections and suggests extensions to bias, redshift-space distortions, and potential higher-order reconstructions to further improve BAO-based distance measurements.

Abstract

Recently Eisenstein and collaborators introduced a method to `reconstruct' the linear power spectrum from a non-linearly evolved galaxy distribution in order to improve precision in measurements of baryon acoustic oscillations. We reformulate this method within the Lagrangian picture of structure formation, to better understand what such a method does, and what the resulting power spectra are. We show that reconstruction does not reproduce the linear density field, at second order. We however show that it does reduce the damping of the oscillations due to non-linear structure formation, explaining the improvements seen in simulations. Our results suggest that the reconstructed power spectrum is potentially better modeled as the sum of three different power spectra, each dominating over different wavelength ranges and with different non-linear damping terms. Finally, we also show that reconstruction reduces the mode-coupling term in the power spectrum, explaining why mis-calibrations of the acoustic scale are reduced when one considers the reconstructed power spectrum.

Figures (3)

• Figure 1: The damping scale at $z=0$ as a function of the maximum wavenumber for the linear (solid) and non-linear (dashed) power spectra. Note that the dominant contribution to the damping scale come from linear motions.
• Figure 2: The ratio of $\Sigma_{ss}$, $\Sigma_{sd}$ and $\Sigma_{dd}$ to $\Sigma$, as a function of the Gaussian smoothing scale, $R$. Note that for no smoothing, $\Sigma_{ss}=\Sigma$ and $\Sigma_{dd}=0$, while for infinite smoothing, $\Sigma_{dd}=\Sigma$ with $\Sigma_{ss}=0$.
• Figure 3: The damping of the linear power spectrum for the nonlinear power spectrum (dashed line), and the reconstructed power spectrum (Eq. \ref{['eq:damptransform']}, solid line, assuming a smoothing scale $R=5\,h^{-1}$Mpc). The dotted lines decompose the reconstructed damping into the leading contributions from its $P_{ss}$, $P_{sd}$ and $P_{dd}$ components These curves have been calculated assuming $z=0$.