Removing BAO-peak Shifts with Local Density Transforms
  Large-scale bulk flows in the Universe distort the initial density field,
broadening the baryon-acoustic-oscillation (BAO) feature that was imprinted
when baryons were strongly coupled to photons. Additionally, there is a small
shift inward in the peak of the conventional overdensity correlation function,
a mass-weighted statistic. This shift occurs when high density peaks move
toward each other. We explore whether this shift can be removed by applying to
the density field a transform (such as a logarithm) that gives fairer
statistical weight to fluctuations in underdense regions. Using
configuration-space perturbation theory in the Zel'dovich approximation, we
find that the log-density correlation function shows a much smaller inward
shift in the position of the BAO peak at low redshift than is seen in the
overdensity correlation function. We also show that if the initial, Lagrangian
density of matter parcels could be estimated at their Eulerian positions,
giving a displaced-initial-density field, its peak shift would be even smaller.
In fact, a transformed field that accentuates underdensities, such as the
reciprocal of the density, pushes the peak the other way, outward. In our
model, these shifts in the peak position can be attributed to shift terms,
involving the derivative of the linear correlation function, that entirely
vanish in this displaced-initial-density field.
