**Authors:** Christopher Pilot

A model is presented where the quintessence parameter, w, is related to a time-varying gravitational constant. Assuming a present value of w = -.98, we predict a current variation of Ġ/G = - .06 H0, a value within current observational bounds. H0 is Hubble’s parameter, G is Newton’s constant and Ġ 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, albeit at a much slower rate. 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 (we assume a connection exists). To formalize and solidify our model, we give two distinct parametrizations of G with respect to “a”, the cosmic scale parameter. We treat G-1 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 parametrization for G-1 is motivated by a charging capacitor; the second treats G-1(a) by analogy to a magnetic response, i.e., as a Langevin function. Both parametrizations, even though very distinct, give a remarkably similar tracking behavior for w(a), but not of the conventional form, w(a) = w0 + wa (1-a), which can be thought of as only holding over a limited range in “a”. Interestingly, both parametrizations indicate the onset of G formation at a temperature of approximately 7 *1021 degrees Kelvin, in contrast to the ΛCDM model where G is taken as a constant all the way back to the Planck temperature, 1.42 * 1032 degrees Kelvin. 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 ΛCDM model, except in the very early universe, as we shall demonstrate. In fact, in the limit where w approaches -1, Ġ/G vanishes, and we are left with the concordance model. Within our framework, the emergence of dark energy over matter at a scale of a ≈ .5 is that point where G-1 increases noticeably to its current value G0-1. This weakening of G to its current value G0 is speculated as the true cause for the observed unanticipated acceleration of the universe.

**Comments:** 38 Pages. already published;Pilot, C, 2018, Is Quintessence an Indication of a Time-Varying Gravitational Constant?, https://arxiv.org/abs/1803.06431 , Journal of High Energy Physics, Gravitation and Cosmology (JHEPGC) JHEPGC Vol 5 No 1 (2019)

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