Quoting from Gribbin and Rees' COSMIC COINCIDENCES.
"A COSMIC CONNECTION
The same coincidence (concerning the weak force---see Coincidence Two) crops up earlier in the life of the Universe. It is the strength of the weak force that decides how much hydrogen is processed into helium in the Big Bang. It requires a rather precise fine-tuning to avoid a runaway in one direction or the other--make the force slightly stronger and no helium would have been prodcued; make it slightly weaker and nearly ALL the baryons would have been converted into helium in the Big Bang. A universe in which stars were initially made only of hydrogen might not be so very different from our own; but if all the stars were originally composed of helium, they would have burnt out more quickly, perhaps not giving life time to evolve on any planets that formed (if life can indeed develop without hydrogen present to form water). The condition that some stars go through a supernova phase (triggered by a neutrino- boosted shock) is essentially the same as the condition that there be an interesting amount of cosmological helium production. The weak force seems to be just about as weak as it can be in order to avoid all the original hydrogen being converted into helium. Supernovae might still work (exploding by a different mechanism) if the force were a little stronger, but if the force were weaker the neutrinos could not drive any kind of explosion; the Universe would be even more comfortably by hydrogen (baryonically speaking) by hydrogen if the force were a little stronger; but the window of opportunity for a universe in which there is SOME helium AND exploding supernovae, is very narrow.
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