  We investigate the large-scale clustering and gravitational interaction of
baryons and dark matter (DM) over cosmic time using a set of collisionless
N-body simulations. Both components, baryons and DM, are evolved from distinct
primordial density and velocity power spectra as predicted by early-universe
physics. We first demonstrate that such two-component simulations require an
unconventional match between force and mass resolution (i.e. force softening on
at least the mean particle separation scale). Otherwise, the growth on any
scale is not correctly recovered because of a spurious coupling between the two
species at the smallest scales. With these simulations, we then demonstrate how
the primordial differences in the clustering of baryons and DM are
progressively diminished over time. In particular, we explicitly show how the
BAO signature is damped in the spatial distribution of baryons and imprinted in
that of DM. This is a rapid process, yet it is still not fully completed at low
redshifts. On large scales, the overall shape of the correlation function of
baryons and DM differs by 2% at z = 9 and by 0.2% at z = 0. The differences in
the amplitude of the BAO peak are approximately a factor of 5 larger: 10% at z
= 9 and 1% at z = 0. These discrepancies are, however, smaller than effects
expected to be introduced by galaxy formation physics in both the shape of the
power spectrum and in the BAO peak, and are thus unlikely to be detected given
the precision of the next generation of galaxy surveys. Hence, our results
validate the standard practice of modelling the observed galaxy distribution
using predictions for the total mass clustering in the Universe.
