  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.
