The Standard Model Constants Are Constant

The available evidence constrains changes in the strong force coupling constant over time (implicitly, through the quantum chromodynamics energy scale lambda QCD) to a value consistent with zero to high precision, from a robust set of four different sets of data going all of the way back to Big Bang Nucleosynthesis which happens about fifteen minutes after the Big Bang. 

The constraint from atomic clocks of 3.2 ± 3.5 parts per 10^17 per year, when the age of the universe is about 1.38 x 10^10 years, implying a maximum difference of 230 ± 250 parts per billion over the entire age of the universe. The constraint from a natural nuclear reactor on Earth that started to react 1.8 billion years ago is slightly more strict at less than 72 parts per billion over the entire age of the universe. A proposed extension of the paper would tighten that constraint by four orders of magnitude.

Of course, the strong force coupling constant, like all of the other experimentally determined Standard Model constants, run with energy scale, so when the universe was very hot, not so long after the Big Bang, its value at the prevailing temperature of the universe would have been smaller, because the strong force coupling is weaker at higher energies. The relationship between energy-scale and the strength of the strong force coupling constant is known exactly in the Standard Model and has been corroborated by particle accelerator experiment data.

This is also what efforts to determine the electromagnetic force coupling constant (i.e. the Fine Structure Constant) and electron and quark mass ratios, using astronomy to determine those ratios at high redshifts, has found.

Laboratory and astrophysical tests of ''constant variation'' have so far concentrated on the dimensionless fine-structure constant α and on the electron or quark mass ratios Xe,q=me,q/ΛQCD, treating the QCD scale ΛQCD as unchangeable. 

Certain beyond Standard Model frameworks, most notably those with a dark matter or dark energy scalar field ϕ coupling with the gluon field, would make ΛQCD itself time dependent while leaving α and the electron mass untouched. Under the minimal assumption that this gluonic channel is the sole ϕ interaction, we recast state-of-the-art atomic clock comparisons into δΛQCD/ΛQCD=(3.2 ± 3.5) × 10^−17 yr^−1 limits, translate the isotope yields of the 1.8-Gyr-old Oklo natural reactor into a complementary geophysical limit of |δΛQCD/ΛQCD| < 2 × 10^−9 over that time span, corresponding to the linear drift limit |δΛQCD/ΛQCD| < 1 × 10^−18 yr^−1, and show that the proposed 8.4 eV 229Th nuclear clock would amplify a putative ΛQCD drift by four orders of magnitude compared with present atomic clocks. We also obtain constraints from quasar absorption spectra and Big Bang Nucleosynthesis data.

V. V. Mansour, A. J. Mansour, "Constraints on the Variation of the QCD Interaction Scale ΛQCD" arXiv:2508.07266 (August 10, 2025) (derivatives in the abstract above are shown with sigma notation rather than in the original superscript dot notation, because dot notation is hard to render in the blogger interface).