Reconstructing Baryon Oscillations: A Lagrangian Theory Perspective

TL;DR

This paper reformulates a galaxy power spectrum reconstruction method within the Lagrangian framework, showing it reduces non-linear damping and mode coupling, thereby improving baryon acoustic oscillation measurements.

Contribution

It provides a Lagrangian perspective on reconstruction, clarifying its effects and proposing a multi-component model for the reconstructed power spectrum.

Findings

Reconstruction does not fully recover the linear density field at second order.

It reduces damping of oscillations, improving BAO signal clarity.

Reconstruction decreases mode-coupling, reducing calibration errors.

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.