Dark matter is a supersolid that fills 'empty' space, strongly interacts with ordinary matter and is displaced by ordinary matter. What is referred to geometrically as curved spacetime physically exists in nature as the state of displacement of the supersolid dark matter. The state of displacement of the supersolid dark matter is gravity.
The supersolid dark matter displaced by a galaxy pushes back, causing the stars in the outer arms of the galaxy to orbit the galactic center at the rate in which they do.
Displaced supersolid dark matter is curved spacetime.
Another way to think of this is that spacetime has mass. Spacetime and dark matter are both referring to the same 'stuff'. The stuff is a supersolid that is displaced by ordinary matter.
The Earth displaces the 'stuff'. The displaced 'stuff' pushes back. The displaced 'stuff' pushing back is gravity.
Curved spacetime = Geometrical representation of gravity.
Displaced supersolid dark matter = Physical representation of gravity.
The supersolid dark matter displaced by a galaxy pushes back, causing the stars in the outer arms of the galaxy to orbit the galactic center at the rate in which they do.
Displaced supersolid dark matter is curved spacetime.