Bounds upon Graviton Mass: Post-Newtonian Corrections to Gravitational Potential Fields

Abstract

The author presents a post-Newtonian approximation based upon an earlier argument in a paper by Clifford Will as to Yukawa revisions of gravitational potentials, in part initiated by gravitons having explicit mass dependence in their Compton wave length.  Prior work with Clifford Will’s idea was stymied by the application to binary stars and similar astrophysical objects, with non-useful frequencies topping off near 100 Hertz, thereby rendering Yukawa modifications of Gravity due to gravitons effectively an experimental curiosity not testable with any known physics equipment.  This work improves on those results. Furthermore; we argue in favor of both a non-zero initial radius of the universe, using Steven K. Kauffmann’s work and also try to make the case for a non-zero graviton mass. We use Salvoy’s 1983 paper to argue in favor of both a non-zero initial radius of the universe, and non-zero graviton mass (i.e. - heavy gravitons). We claim that a non-zero initial radius (of the universe) supports the massive graviton hypothesis.  This is the main point of this paper. We observe that Gravitinos in the Electroweak era, all 108 – 1012 of them, have an (almost) invariant energy from the beginning of cosmology. This invariant energy constitutes an initial energy value at the start of the universe which can be used to obtain, at the onset of inflation, Kauffmann’s lower bound to a non-zero initial radius of the universe.