Comment on a unified theory of weak and strong gravity

Abstract

In a recent paper CHELA-FLORES (1) considered the unification of the concepts of strong and weak gravity through the use of two scalar fields interacting with the usual 9. tensor gravity. The interaction term in the action is of the form (r + ~ ) R , where ~8 and ~w are the strongand weak-gravity scalars respectively. A correspondence principle was discussed where in the l imit that nuclear forces are negligible (beyond a few femtometers) % << ~w, while in the l imit of strong-gravity dominance ~% << ~08. By gauging the fields as in a theory by FREUND (2), it was shown that the effect of spontaneously broken discrete symmetries C and CP of the gauge field will be of the correct order of magnitude for the reaction Kz-+ 27: in the l imit of strong gravity. This is in opposition to the phenomenological replacement of weak gravity by strong gravity as was done in ref. (2). However there are some problems with the Chela-Flores theory in connection with strong gravity. The scalar field in this limit is supposed to exhibit the Yukawa behavior of the nuclear force. This implies that the field representing strong gravity must be a massive field. On the other hand, the presence of a massive field would spoil the scale invariance of the theory. In this note we would like to show how these remarks can be reconciled by the use of spontaneously broken scale symmetry (a). Due to the presence of a dilaton field (which we identify with the long-range weak-gravity scalar) the masses of particles are spontaneously generated while the overall action remains scale invariant . To demonstrate how this mechanism works we start with the following action in which scale symmetry is explicity broken: