Liouville Field Theory and Dark Matter
  One of the most intriguing unsolved problems in modern cosmology involves the nature of the observed dark matter in the universe. Various hypothetical particles have been postulated as the source of the dark matter, but as of yet none of these particles have been observed. In this paper I present an alternative view. The observations indicate the presence of a new force that is much weaker than gravity on small scales and stronger than gravity on large scales. This new force is described by a Liouville field that consists of a scalar field with an exponential potential. The solutions have a Newtonian behavior on small scales and produce forces that are weak compared to gravity. On large scales the field has a logarithmic behavior and will therefore produce flat rotation curves. The Liouville field may therefore be able to account for the observations that are usually taken to imply the existence of dark matter. 
Dan N. Vollick