How a tiny change in a particle-physics parameter could affect the early universe’s neutrons

Neutrons did not simply stop changing into protons at one instant in the early universe. As the cosmos cooled, weak-interaction reactions gradually became less effective compared with the universe’s expansion. Neutrons could still decay, while some reactions continued to convert protons back into neutrons. The final neutron supply available for Big Bang nucleosynthesis (BBN), the formation of light nuclei, reflects this competition.

In a preprint, Cheng Tao Yang and Johann Rafelski examine how that supply would change if the weak interaction strength in the early universe differed slightly from its laboratory value. Their focus is the Fermi constant, a parameter that sets the strength of weak interactions. In the authors’ calculation, radiative corrections make this constant depend on the Weinberg angle, a parameter describing electroweak interactions.

The central question is conditional: if the effective Weinberg angle in the hot primordial plasma shifted, how would the resulting change in weak reaction rates affect neutron abundance and neutron lifetime? The paper does not establish that such a shift actually occurred.

Following neutrons through a cooling plasma

Rather than estimate the neutron fraction from a single freeze-out temperature and then let neutrons decay, the authors set up a kinetic population equation. In plain language, this tracks the neutron fraction as a balance of processes that add and remove neutrons over time. They calculate neutron–proton conversion reactions, neutron decay, and the changing expansion rate of the universe.

Their treatment also includes effects of the surrounding plasma. Electrons and neutrinos can block some neutron-decay products, slowing decay compared with the vacuum case. The calculation accounts for photons being reheated as electron–positron pairs disappear, while already-decoupled neutrinos cool differently. These details affect both reaction rates and the link between temperature and cosmic time.

The authors vary the Weinberg angle as an external parameter, using values intended to span a range discussed in connection with measurements at different energy scales. They then calculate the neutron fraction across the cooling period, including the transition when weak reactions no longer keep pace with expansion. This is a model-based sensitivity study, not a measurement of the angle in the early universe.

What the model finds

At higher temperatures, weak reactions maintain a near-equilibrium balance between neutrons and protons. In this regime, the paper says, the neutron fraction depends only weakly on the assumed angle: the overall weak-interaction strength largely cancels in the balance between conversion rates.

The situation changes as the universe cools and reaction rates compete with expansion. The kinetic correction to the near-equilibrium result depends on the size of the weak rates relative to the Hubble expansion rate. Since the authors’ parameterization links those rates to the Weinberg angle, the calculated neutron fraction becomes more sensitive to that angle. The paper reports that the fraction decreases as the angle increases in the range it studies.

The authors also find that expansion-related kinetic effects matter to the neutron abundance at the onset of BBN. In their calculation, the elapsed time to a condition associated with deuteron formation is longer than in a simplified treatment, and the neutron fraction there is lower by about 6%. This is a result within their model, before including neutron capture into nuclei as a depletion process. The paper says such nuclear reactions could be added to the kinetic framework, but does not present a full nuclear-network calculation here.

A possible explanation is not evidence

The authors connect their sensitivity study to the difference between neutron-lifetime measurements using “beam” and “bottle” methods. They suggest, explicitly without direct evidence, that a small environmental dependence of the Weinberg angle might contribute to the disagreement. That remains speculation: the paper does not demonstrate that the angle changes with temperature or experimental conditions, and it does not rule out unresolved experimental systematics.

This distinction matters because the calculation takes the angle’s possible variation as an input. The authors describe their arguments for environmental dependence as intuitive and acknowledge that a theoretically complete account of how the angle might depend on temperature remains to be developed. Their results show what follows if the parameter shifts under their assumptions; they do not show that nature supplies that shift.

The authors also identify limits in the plasma treatment. They omit some finite-temperature corrections, including thermal mass shifts and changes to certain radiative factors, and cite estimates suggesting omitted effects on neutron abundance at roughly the 0.1–0.5% level in the temperature range considered. Their precision claims therefore depend on modeling choices as well as on the proposed angle variation.

This is a preprint: the manuscript says it was submitted to Particles for possible publication, so it should not be treated as a peer-reviewed result. Its source text is also an extracted version of the paper, which can lose formatting in equations and figures. The safest takeaway is narrower than the title’s speculative motivation: a detailed kinetic calculation finds that the predicted pre-BBN neutron fraction can respond to changes in weak-interaction strength during the period when cosmic expansion and weak reactions compete. Whether the Weinberg angle actually varies in the primordial plasma—and whether that could explain laboratory measurements—remains unestablished.