Is Quintessence an Indication of a Time-Varying Gravitational Constant?

Abstract

A model is presented where the quintessence parameter, w, is related to a time-varying gravitational constant. Assuming a present value of w equals -.98, we predict a current variation of G dot/G = -.06 H0. H0 is Hubbles parameter, G is Newtons constant and G dot is the derivative of G with respect to time. Thus, G has a cosmic origin, is decreasing with respect to cosmological time, and is proportional to H0, as originally proposed by the Dirac-Jordan hypothesis. Within our model, we can explain the cosmological constant fine-tuning problem, the discrepancy between the present very weak value of the cosmological constant, and the much greater vacuum energy found in earlier epochs. To formalize and solidify our model, we give two distinct functions of G(a), the cosmic scale parameter. We treat inverse G as an order parameter, which vanishes at high energies; at low temperatures, it reaches a saturation value, a value we are close to today. Our first function for inverse G is motivated by a charging capacitor; the second treats inverse G by analogy to a magnetic response. Both functions, even though very distinct, give a remarkably similar tracking behavior for w(a). Interestingly, both functions indicate the onset of G formation at a temperature of approximately 7 *1021 degrees Kelvin, in contrast to the concordance model. At the temperature of formation, we find that G has increased to roughly 4*1020 times its present value. For most of cosmic evolution, however, our variable G model gives results similar to the predictions of the concordance model, except in the very early universe, as we shall demonstrate. Within our framework, the weakening of G to its current value G0 is speculated as the true cause for the observed unanticipated acceleration of the universe.