Past exam of the mathematics course of the University of Cambridge 2005 ii Paper 1 10D c Solution Created 2026-09-24 Updated 2026-10-14
If the weak-rate coefficient is reduced, equality with the expansion rate occurs at a higher temperature, since scales as that coefficient times . The freeze-out temperature and interaction strength relation is . The frozen neutron-to-proton ratio is then closer to one, so the primordial helium mass fraction increases, potentially approaching unity if nearly equal numbers survive to nucleosynthesis. If the same weaker interaction also slows free-neutron decay, it reinforces this trend; changing conversion rates alone would instead require a separate treatment of the decay interval.
Less primordial hydrogen means less hydrogen fuel and, for otherwise comparable stellar physics, helium enrichment raises the mean molecular weight, tending to make a fixed-mass star hotter and more luminous and to shorten its hydrogen-burning lifetime. A genuinely weaker weak interaction also changes proton-proton fusion itself, so a quantitative lifetime cannot be inferred from composition alone. Much less hydrogen and fewer long-lived suitable stars would alter planet formation, water availability and the timescales needed for life on Earth. These are physical implications of the changed initial composition, not a numerical prediction of habitability from the helium fraction alone.