Is gravity a function of the geometry (astrometry?) of spacetime as Einstein predicted or is it the function of a force-carrier particle (graviton) as suggested by the Soviets?

The answer is important because a gravity drive powered craft is conceivable if gravity is created by gravitons and one can generate enough of them ( assuming we knew what gravitons were and how to make them ).

However, if gravity is a function of the curvature of spacetime, then the only way to create gravity is to create mass, and that makes the prospect of a gravity drive more difficult - as in: it's difficult to keep several Jupiter masses in your pocket.