## B9 Keeping the gravitational constant positive

We can gain more insights into the interpretation of the physics that is implied for us by CCC, if we examine the interaction between the mass-less gravitational source fields, as described by Tab, and the gravitational field (or 'graviton field') tyabcd, as implied by the equation (P&R 4.10.12) of A5, taken in 'hatted form', and rewritten in terms of w = - H-1. We have

V£(- w ^abcd) = 4nGVg'((- wfTcDA-B-), from which we derive the equivalent equation, in terms of the 'unhatted' quantities,

We note that this equation remains well behaved as w increases smoothly through zero (from negative to positive). This illustrates the fact that the family of partial differential equations governing the evolution of the entire system, in terms of the g-metric, does not encounter difficulties when passing through k, from VA to Vv.

Let us imagine that we revert to use of the original g-metric when we proceed into Vv. Then (apart from the initial 'glitch' at k), the picture that our classical equations would provide us with, for the evolution of the space-time Vv, would be a collapsing universe model, contracting in a reverse-exponential way, inwards from infinity, seeming to be very much like a time-reverse of what is envisaged for the remote future of our own universe. However, there is an important issue of interpretation here, because when w changes sign, from negative to positive, the 'effective gravitational constant' (as seen particularly in the - Gw in the above formula when this first term on the right begins to dominate as w gets larger), has changed sign after kis crossed.[B12] The alternative interpretation that CCC presents us with is that because of considerations of physical consistency with quantum field theory, etc., this particular interpretation (with a negative gravitational constant) of the physics in the early Vv region cannot be properly maintained in a physical way when gravitational interactions become important. The point of view of CCC

is that, instead, it becomes more appropriate, as we continue to proceed into the V v region, to adopt the physical interpretation provided by the g-metric, where the now-positive conformal factor w replaces the now-negative H, and the effective gravitational constant now becomes positive again.

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