Cosmology with time-varying G

It is shown that a Universe with time-varying gravitational ''constant'' G necessarily implies creation if the rest mass of matter particles msub(rho) is constant. In this case, from Einstein's field equations, the conditions for energy-momentum propagation are nabla . (GTsup(μν)=O from which matter and photon propagation equations are derived. Free matter particle propagation is not affected by creation that is given by GNsub(rho)msub(rho)=const, where Nsub(rho) is the number of matter particles within a proper volume. This relation introduces explicitly the rest mass of the Universe into the field equations. It is found that at an age t=10-40sub(t)0, of the order light takes to travel a proton size, Planck's units become of the order of the proton's mass msub(rho), size rsub(rho), and time rsub(rho)/c. Hence, matter particles at this age are quantum black holes. Evaporation of these quantum black holes at this age gives a background blackbody radiation that, red shifted to present time t0, gives the present cosmic microwave background. A cosmological model of the Friedmann type is constructed in which the three results for the age of the Universe, i.e., radioactive decay, Hubble's constant, and stellar evolution are brought together. (author)