  In this paper we entertain a Machian setting where local physics is
non-locally affected by the whole Universe, taking the liberty to identify the
local (``Newton's bucket'') with our visible Universe, and the whole Universe
(Mach's ``fixed stars'') with the global Universe beyond our horizon.
Crucially, we allow for the two to have different properties, so that we are
beyond the traditional FRW setting. For definiteness we focus on theories where
non-locality arises from evolution in the laws of physics in terms of spatially
global time variables dual to the constants of Nature. Since non-local theories
are foliation-dependent, the {\it local} (but not the global) Hamiltonian
constraint is lost. This is true not only while non-locality is taking place,
but also after it ceases: the local Hamiltonian constraint is only recovered up
to a constant in time, keeping a memory of the integrated past non-locality. We
show that this integration constant is equivalent to preserving the local
Hamiltonian constraint and adding an extra fluid with the same cosmological
properties as conventional pressureless dark matter. The equivalence breaks
down in terms of clustering properties, with the new component attracting other
matter, but not budging from its location. This is the ultimate ``painted-on''
dark matter, attracting but not being attracted, and nailing down a preferred
frame.
