  We study the effect of baryons on the inner dark matter profile of the first
galaxies using the First Billion Years simulation between z=16-6 before secular
evolution sets in. Using a large statistical sample from two simulations of the
same volume and cosmological initial conditions, one with and one without
baryons, we are able to directly compare haloes with their baryon-free
counterparts, allowing a detailed study of the modifications to the dark matter
density profile due to the presence of baryons during the first billion years
of galaxy formation. For each of the ~ 5000 haloes in our sample we quantify
the impact of the baryons using eta, defined as the ratio of dark matter mass
enclosed in 100 pc in the baryonic run to its counterpart without baryons.
During this epoch of rapid growth of galaxies, we find that many haloes of
these first galaxies show an enhancement of dark matter in the halo centre
compared to the baryon-free simulation, while many others show a deficit. We
find that the mean value of eta is close to unity, but there is a large
dispersion, with a standard deviation of 0.677. The enhancement is cyclical in
time and tracks the star formation cycle of the galaxy; as gas falls to the
centre and forms stars, the dark matter moves in as well. Supernova feedback
then removes the gas, and the dark matter again responds to the changing
potential. We study three physical models relating the motion of baryons to
that of the dark matter: adiabatic contraction, dynamical friction, and rapid
outflows. Abridged, see text for full abstract
