  We study the cosmology of a three-brane in a specific five-dimensional
scalar-gravity (i.e. soft-wall) background, known as the linear dilaton
background. We discover that the Friedmann equation of the brane-world
automatically contains a term mimicking pressureless matter. We propose to
identify this term as dark matter. This dark matter arises as a projection of
the bulk black hole on the brane, which contributes to the brane Friedmann
equation via both the Weyl tensor and the scalar stress tensor. The nontrivial
matter-like behavior is due to an exact cancellation between the Weyl and
scalar pressures. We show that the Newtonian potential only receives a mild
short-distance correction going as inverse distance squared, ensuring
compatibility of the linear dilaton brane-world with observed 4D gravity. Our
setup can be viewed as a consistent cosmological description of the holographic
theories arising in the linear dilaton background. We also present more general
scalar-gravity models where the brane cosmology features an effective energy
density whose behavior smoothly interpolates between dark radiation, dark
matter and dark energy depending on a model parameter.
