Cosmological dark matter from a bulk black hole

We study the cosmology of a 3-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 matterlike behavior is due to an exact cancellation between the Weyl and scalar pressures. We show that the Newtonian potential receives only 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.