Looking for a specific theory concerning Dark Matter I am looking for the name of a theory positing that "empty" space itself is not empty, but has substance, and that "fabric" or "substance" is actually what we call Dark Matter.  In theory, dark matter does not have electromagnetic force nor emit or absorb light (like "empty" space) and does not interact with the material universe, except by way of gravity.  In this theory "empty" space (dark matter?) does however distort and bend to gravity.  In theory galaxies spin faster than their observable matter's gravity should allow, yet each body of mass, and indeed solar system has a sphere or halo of condensed "empty" space around it due to the affects of gravity. If "empty" space itself has gravity, the theory im looking for would propose that Dark Matter may in fact be the fabric of space itself, and contributes to the total gravity of a body of mass as it condenses around it. 
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I am looking for the name of a theory positing that "empty" space itself is not empty

Rather surprisingly, it's called General Relativity. See the Einstein digital papers where in his 1920 Leyden Address Einstein said this: 
"This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that 'empty space' in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν) has, I think, finally disposed of the view that space is physically empty".

but has substance, and that "fabric" or "substance" is actually what we call Dark Matter. 

Einstein definitely thought of space as a "fabric". Google on general relativity fabric. However people don't think of it as dark matter. I think they should however remember what Einstein said in the Foundation of the General Theory of Relativity: "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". This is an example of something you can't see causing gravity. It isn't dark matter in the sense that it consists of matter particles, but the spatial energy does have a mass equivalence.   

In theory, dark matter does not have electromagnetic force nor emit or absorb light (like "empty" space) and does not interact with the material universe, except by way of gravity. 

Nor does the spatial energy of a gravitational field. 

In this theory "empty" space (dark matter?) does however distort and bend to gravity. In theory galaxies spin faster than their observable matter's gravity should allow, yet each body of mass, and indeed solar system has a sphere or halo of condensed "empty" space around it due to the affects of gravity. If "empty" space itself has gravity, the theory I'm looking for would propose that Dark Matter may in fact be the fabric of space itself, and contributes to the total gravity of a body of mass as it condenses around it. 

I don't think there's any such theory in existence, but I imagine there will be. All it will take is a combination of general relativity and the standard model of cosmology. Einstein described a gravitational field as space that was "neither homogeneous nor isotropic". The raisin-cake analogy says space expands between the galaxies but not within. So conservation of energy suggests the space around a gravity becomes more and more inhomogeneous. And don't forget: according to Einstein, inhomogeneous space is what a gravitational field is. Have a look at http://arxiv.org/abs/1209.0563 which talks about inhomogeneous and interacting vacuum energy. It doesn't say much about dark matter, but IMHO it's going in the right direction.  
