Cosmological vacuum solutions in Brans and Dicke's scalar-tensor theory

The exact cosmological vacuum solutions of Brans and Dicke's scalas-tensor theory are derived when a power law is valid between the gravitational constant κ and the radius of curvatureR of the universe. There exist even in the case of the closed 3-dimensional space of positive curvature solutions with increasingR and κ with respect to the age of the universe, whereby the freely available parameter ω of the scalar-tensor theory can take all values greater than −3/2. Such solutions are contrary to Dirac's hypothesis as well as to Einstein-Mach's principle.