In Chapter 9C of the 'Critique' we considered relatively small increases in the strong force, increasing gs by 10% - 40%. This is sufficient to bind the diproton. However, we showed that, contrary to the claims commonly made, no diprotons would be formed in the Big Bang. Moreover, we argued that stars which could sustain life on planets would still be possible, though different from those of our universe. In Chapter 9 of the 'Critique' we showed that a sufficient reduction in gs would lead to a universe with no stable nuclei, and hence no chemistry. However we did not identify an upper bound for gs in Chapter 9. The oft claimed upper bound based on diproton stability has been shown to be spurious in Chapter 9C. So we must ask - is there an upper bound on gs for a complex universe?
In this Chapter we make the observation that if gs is increased by more than ~40% then deuterium is stable before ~1 second. This is the period when the leptonic reactions which interconvert protons and neutrons are still active. Thus, at small fractions of a second, the proton:neutron ratio will be less than the 87%:13% level that it attains prior to nucleosynthesis in this universe (at around 2 minutes or so). When deuterium becomes stable, the existing free neutrons are rapidly captured by protons to form deuterium, and subsequently helium. The hydrogen fraction of the primordial universe is determined simply by how many protons are left over. Thus, if deuterium is stable when the proton:neutron ratio is close to 50%:50%, then the universe becomes virtually all helium and no hydrogen. This is exactly the catastrophic scenario that other authors had envisaged as resulting from diproton stability - and which we have discredited.
Thus, for increases of gs sufficiently greater than 40%, there is potentially a mechanism which would result in a universe with very little hydrogen, quite independent of diproton stability. In this Chapter we investigate the credibility of this mechanism. We find that increasing gs by a factor of 4.3 results in the hydrogen fraction falling from 75% to 3%. Similarly, increasing gs by a factor of 2.7 results in the hydrogen fraction falling from 75% to 10%. These are far larger changes in gs than the usually claimed upper bound. Moreover, it is not entirely clear that a universe with 3% or 10% hydrogen are incompatible with complex chemistry and life.
Consequently, this upper bound on gs is rather a soft bound, of Type D.
Finally, we note that in this scenario virtually all the neutrons get 'cooked' into helium-4. However, it is difficult to be sure that nucleosynthesis stops there. If lithium-5 and/or beryllium-8 are stable in such a universe, then quite a rich mixture of elements might result from the Big Bang, as originally envisaged by Gamow.
