This paper introduces the Hidden Valley simulations, a set of
trillion-particle N-body simulations in gigaparsec volumes aimed at intensity
mapping science. We present details of the simulations and their convergence,
then specialize to the study of 21-cm fluctuations between redshifts 2 and 6.
Neutral hydrogen is assigned to halos using three prescriptions, and we
investigate the clustering in real and redshift-space at the 2-point level. In
common with earlier work we find the bias of HI increases from near 2 at z = 2
to 4 at z = 6, becoming more scale dependent at high z. The level of
scale-dependence and decorrelation with the matter field are as predicted by
perturbation theory. Due to the low mass of the hosting halos, the impact of
fingers of god is small on the range relevant for proposed 21-cm instruments.
We show that baryon acoustic oscillations and redshift-space distortions could
be well measured by such instruments. Taking advantage of the large simulation
volume, we assess the impact of fluctuations in the ultraviolet background,
which change HI clustering primarily at large scales.