Cosmological Dark Matter from a Bulk Black Hole

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.