Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 9D / c / Solution

A larger $\eta$ increases the deuterium fraction at fixed temperature, so the bottleneck ends at a higher temperature and earlier time. With weak decoupling unchanged, fewer free neutrons then beta-decay before nuclear reactions bind them. Since primordial helium production is neutron-limited, the baryon-density effect on primordial helium makes $Y_{\mathrm{He}}$ larger than the standard value.