  We examine the scale dependence of dark matter, halo and galaxy clustering on
very large scales (0.01<k[h/Mpc]<0.15), due to non-linear effects from dynamics
and halo bias. We pursue a two line offensive: high resolution numerical
simulations are used to establish several new results, and an analytic model is
developed to understand their origins. Our simulations show: (i) that the z=0
dark matter power spectrum is suppressed relative to linear theory by ~5% on
scales (0.05<k[h/Mpc]<0.075); (ii) that, indeed, halo bias is non-linear over
the scales we probe and that the scale dependence is a strong function of halo
mass. High mass haloes show no suppression of power on scales (k<0.07[h/Mpc]),
and only show amplification on smaller scales, whereas low mass haloes show
strong, ~5-10%, suppression over the range (0.05 <k[h/Mpc] <0.15). Our results
have relevance for studies of the baryon acoustic oscillation features.
Non-linear mode-mode coupling: (i) damps these features on progressively larger
scales as halo mass increases; (ii) produces small shifts in the positions of
the peaks and troughs which depend on halo mass. Our analytic model is
described in the language of the `halo-model'. However, for the first time the
halo-halo clustering term is propagated into the non-linear regime using
`1-loop' perturbation theory and a non-linear halo bias model. We show that,
with bias parameters derived from simulations, the model predictions are in
agreement with the numerical results. We then use the model to explore the
scale dependence of galaxies of different colour and find significant
differences between the power spectra of the two populations. Thus
understanding the scale dependent bias for a given galaxy sample will be
crucial for deriving accurate cosmological constraints. (Abridged)
