  We reformulate Einstein's theory of gravity, isolating the conformal degree
of freedom in a covariant way. This is done by introducing a physical metric
defined in terms of an auxiliary metric and a scalar field appearing through
its first derivatives. The resulting equations of motion split into a traceless
equation obtained through variation with respect to the auxiliary metric and an
additional differential equation for the trace part. As a result the conformal
degree of freedom becomes dynamical even in the absence of matter. We show that
this extra degree of freedom can mimic cold dark matter.
