  We examine effective field theories (EFTs) with a continuum sector in the
presence of gravity. We first explain, via arguments based on central charge
and species scale, that an EFT with a free continuum cannot consistently couple
to standard (i.e. 4D Einstein) gravity. It follows that EFTs with a free or
nearly-free continuum must either have a finite number of degrees of freedom or
nonstandard gravity. The latter claim is realized for holographically-defined
continuum models. We demonstrate this by computing the deviations from standard
gravity in a specific 5D scalar-gravity system that gives rise to a gapped
continuum (i.e the linear dilaton background). We find an $R^{-2}$ deviation
from the Newtonian potential. At finite temperature we find an energy density
with matter-like behavior in the brane Friedmann equation, holographically
induced from the bulk geometry. Thus, remarkably, a brane-world living in the
linear dilaton background automatically contains dark matter. We also present a
slightly more evolved asymptotically-AdS linear dilaton model, for which the
deviations exhibit a transition between AdS and linear dilaton behaviors.
