  We examine local physics in the presence of global variables: variables
associated with the whole of the spacelike surfaces of a foliation. These could
be the (pseudo-)constants of nature and their conjugate times, but our
statements are more general. Interactions between the local and the global (for
example, dependence of the local action on global times dual to constants)
degrades full space-time diffeomorphism invariance down to spatial
diffeomorphism invariance, and so an extra degree of freedom appears. When
these presumably primordial global interactions switch off, the local action
recovers full invariance and so the usual two gravitons, but a legacy matter
component is left over, bearing the extra degree of freedom. Under the
assumption that the preferred foliation is geodesic, this component behaves
like dark matter, except that 3 of its 4 local degrees of freedom are frozen,
forcing its rest frame to coincide with the preferred foliation. The non-frozen
degree of freedom (the number density of the effective fluid) is the survivor
of the extra "graviton" present in the initial theory, and keeps memory of all
the past global interactions that took place in a given location in the
preferred foliation. Such "painted-on" dark matter is best distinguished from
the conventional one in situations where the preferred frame would be
preposterous if all 4 degrees of freedom of dark matter were available. We
provide one example: an outflowing halo of legacy matter with exact escape
speed at each point and a very specific profile, surrounding a condensed
structure made of normal matter.
