Using the new interpretation for mass, the question becomes "How does momentum warp space-time?" Simply, the larger the momentum, p; the smaller, proportionally, the space dimension, x. As shown on the source of particle force page, the reason comes from quantum theory: px=nh. The beauty of this view is that p and x are already fundamentally linked together in quantum theory. Using quantum theory to explain the source for general relativity space curvature is one consequence of this model. It seems almost unreasonable that the largest scale effect is a result of quantum theory. But it isn't farfetched when one remembers that general relativity theory is a local theory. That is the geodesic that particle follows is only dependent on the local space-time curvature, it isn't a force at a distance theory.
Another reason to view gravity as a quantum effect is historical. Nuclear forces are readily seen to be heavily dependent on quantum theory. Theories have already been proposed for quantum gravity. This model like all unification theories assumes the same mechanism applies for all forces. It is already assumed that the same physical principals are uniform through time and space. Generalizing them for use on different size scales isn't that great a leap of intuition.
This concept can also be viewed as the reason for Lorentz contraction in special relativity. When a particle is at rest in normal space relative to other particles, the distance between particles is measured as one value. Once this particle is accelerated to 0.5 c increasing its total momentum, the distance between particles is measured as smaller. The actual amount of this decrease is dependent on the direction one is looking. Now, expanding this concept for a closed hypersphere in normal space, one returns to one's original starting point more quickly as the speed of light is approached. The dimension of the universe seems to shrink along the vector of ones motion. Traveling sufficiently fast, the dimension x can look to be only a meter long, while y and z still remain billions of light years long.