Can Gravitation Have a Finite Range?

Abstract

No acceptable tensor gravitational theory with arbitrarily long but finite range exists. In linear approximation, the infinite-range limit is a scalar-tensor mixture implying an effective matter-matter coupling different from the strictly infinite-range prediction and contradicted by experiment. Compensation of the scalar requires the admixture of a ghost scalar coupling. In the massive version of the full Einstein theory, (a) there are necessarily six rather than the five tensor degrees of freedom, (b) the energy has no lower bound, (c) the infinite-range limit seems not to exist at all, and (d) lowest-order forces are the same as in the massive linearized theory.