Russell Standish wrote:

  Incidently, here's my own theory on the origin of matter. (Special)
  relativistic quantum mechanics delivers the prediction of matter
  being in perfect balance with antimatter - this is well known from
  Dirac's work in the 1930s. However, if spacetime had a nonzero
  curvature, is this not likely to bias the balance between matter
  and antimatter, giving rise to the net presence of matter in our
  universe. It strikes me that "mass curves spacetime" is the wrong
  way of looking at General Relativity - causation should be seen the
  other way - curved spacetime  generates mass. As I mentioned above,
  it is not surprising that spacetime is curved, what is surpising is
  that it is so nearly flat.

Russell, you are confusing antimatter with negative matter/energy. According to convention antimatter has inverted electrical charge and therefore when the amount of matter and antimatter are in equal amount, the net charge is zero. Antimatter, however, has positive mass corresponding to positive energy in the sense of E=mc^2 . Consequently, antimatter as well as matter give space a positive curvature.

Negative matter/energy however are different. If negative matter/energy could exist they would give space a negative curvature. Negative matter/energy may be identical to dark energy.

George Levy

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