Removing BAO-peak Shifts with Local Density Transforms

TL;DR

This paper investigates how local density transforms, like the logarithm, can reduce BAO peak shifts caused by large-scale flows, improving the accuracy of cosmological measurements.

Contribution

It demonstrates that applying a log-density transform significantly diminishes BAO peak shifts in the correlation function, offering a new method to correct for bulk flow distortions.

Findings

Log-density correlation shows smaller BAO peak shift at low redshift.

Displaced-initial-density field further reduces peak shift.

Reciprocal density pushes the peak outward, increasing shift.

Abstract

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.