The impact of wrong assumptions in BAO reconstruction

The process of density field reconstruction enhances the statistical power of distance scale measurements using baryon acoustic oscillations (BAO). During this process a fiducial cosmology is assumed in order to convert sky coordinates and redshifts into distances; fiducial bias and redshift-space-distortion parameters are also assumed in this procedure. We analytically assess the impact of incorrect cosmology and bias assumptions on the post-reconstruction power spectra using low-order Lagrangian perturbation theory, deriving general expressions for the incorrectly reconstructed spectra. We find that the BAO peak location appears to shift only by a negligible amount due to wrong assumptions made during reconstruction. However, the shape of the BAO peak and the quadrupole amplitude can be affected by such errors (at the percent- and five-percent-level respectively), which potentially could cause small biases in parameter inference for future surveys; we outline solutions to such complications.