  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.
