Reconstructing Baryon Oscillations: A Lagrangian Theory Perspective
  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. 
Nikhil Padmanabhan, Martin White, J.D. Cohn