Solution (source code)

= Solution

Under the usual interpretation that the extra force simply slows otherwise adiabatic expansion, without changing reaction rates or injecting particles, \b[the primordial hydrogen mass fraction would be larger]. A smaller <Hubble parameter> makes cooling slower, delays the end of the <deuterium bottleneck>, and permits more <free-neutron decay after freeze-out> before nuclear assembly. If the reduced expansion also keeps weak conversions effective longer, the lower eventual <cosmological weak freeze-out> temperature further reduces the <neutron-to-proton ratio>. Both effects lower the <primordial helium mass fraction> and raise the remaining <hydrogen mass fraction>.

For fixed initial neutron fraction $x_{n,1}=n_n/(n_n+n_p)$, the post-freeze-out estimate is $x_n=x_{n,1}e^{-(t_N-t_1)/\tau_n}$, where $t_N$ is the onset of efficient nuclear assembly. Thus $Y_p\simeq2x_n$ decreases when cooling delays $t_N$. The extra time is the time to reach the nuclear-assembly temperature, not an increase in the specified clock interval $300-1$ seconds. An unspecified force that also reheats the plasma, changes weak rates or causes recollapse would require additional information; the simple expansion-only interpretation is essential to this expectation.