Density-dependent clustering: I. Pulling back the curtains on motions of
  the BAO peak
  The most common statistic used to analyze large-scale structure surveys is
the correlation function, or power spectrum. Here, we show how `slicing' the
correlation function on local density brings sensitivity to interesting
non-Gaussian features in the large-scale structure, such as the expansion or
contraction of baryon acoustic oscillations (BAO) according to the local
density. The sliced correlation function measures the large-scale flows that
smear out the BAO, instead of just correcting them as reconstruction algorithms
do. Thus, we expect the sliced correlation function to be useful in
constraining the growth factor, and modified gravity theories that involve the
local density. Out of the studied cases, we find that the run of the BAO peak
location with density is best revealed when slicing on a $\sim 40$ Mpc/$h$
filtered density. But slicing on a $\sim100$ Mpc/$h$ filtered density may be
most useful in distinguishing between underdense and overdense regions, whose
BAO peaks are separated by a substantial $\sim 5$ Mpc/$h$ at $z=0$. We also
introduce `curtain plots' showing how local densities drive particle motions
toward or away from each other over the course of an $N$-body simulation.
