Origin of the gravitational constant and particle masses in a scale-invariant scalar-tensor theory

Abstract

A viable scalar-tensor theory of gravitation is formulated by imposing global scale invariance to the matter part. Nonvanishing masses $m$ of elementary particles as well as the gravitational constant $G$ emerge through the cosmological background value of the scalar field. The scalar field maintains a dynamical degree of freedom in exchange for conformal invariance enjoyed otherwise by the gravity part. The temporal developments of $G$, $m$, and the scale factor of the Universe are determined simultaneously by solving coupled differential equations. In the simplest single-scalar model the result is not a variable-$G$ theory in the usual sense. Departures from the standard theory occur through the time-dependent cosmological term. Of particular interest among the solutions are the asymptotically standard solutions.