Our lives take place on a cosmological background but the space around is flat with an amazing accuracy. If the size of the Universe were strongly influencing the constants such as the fine structure constant through a power law whose exponent is positive and differs from zero significantly, we would have noticed. If the size of the Cosmos were influencing the constant through a negative power law, the influence is negligible and unmeasurable. The only plausible dependence is a term proportional to the logarithm of the size of the Universe that could appear in the formula for the fine-structure constant (with a small coefficient!), but I am not aware of convincing quintessence models that would lead to such a result. And indeed, quintessence - a scalar field whose potential energy mimicks the cosmological constant - is rather unmotivated anyway, which is an even more serious problem.
What do the observations say?
Let me start with the papers that argue to have found upper bounds - i.e. that argue that the constants are really constant and my beliefs are correct. The list includes observations by Chand, Srianand, and collaborators. They used the Very Large Telescope (VLT) and looked at the spectrum of distant quasars:
These are technically well-known papers. Their final value for the relative time evolution
- d ln(alpha) / dt = d alpha / (dt alpha)
is around zero or so, with error of order
- 1 x 10^{-16} per year.
After ten billion = 10^{10} years, you get at most something like one part per million of relative change in the value of the fine structure constant. Recently, this group has debunked some kind of criticism by measuring things a bit differently. Another team looking at similar things is Quast et al.
Actually, you don't need astronomers to measure things. Patient experimenters in a lab are enough. Peik et al. measured the frequencies of some spectral lines of Cesium twice, with a 2.8 year delay, and they also obtained morally zero for the evolution of the fine structure constant, although with 20 times worse accuracy than the quasar measurements above.
Keith Olive et al. combine the astronomical and lab measurements to argue that the upper bound for the change during the existence of the Solar system is again one part per million. You know, sometimes people argue that they need an evolving alpha to obtain the right concentration of magnesium isotopes, but Keith Olive et al. think differently.
When the first nuclei were born
The Big Bang Nucleosynthesis, the process during the era when the Universe was less than three minutes old, when every mile today was one millimeter then, and when the temperature was so high that the nuclei were created out of thermal fluctuations of the strongly interacting mess, predicts a certain relative abundance of light elements - and these predictions agree with observations.
This is our most archaic directly verified prediction of the Big Bang cosmology - that goes to a few minutes after the moment of creation. Inflation occured much earlier, but we only measure its indirect effects as imprinted in the Cosmic Microwave Background that was born when the Universe was 300,000 years old and most accurately measured by the WMAP satellite.
A significant time-dependence of the constants would ruin this beautiful agreement. This imposes other bounds, see e.g. Cyburt, Fields, Olive, and Skillman. They discuss the time evolution of Newton's constant, too. Another recent paper about the nucleosynthesis bounds is by Nidal Chamoun, Susana female Landau, Mercedes E. Daimlerchrysler Mosquera, and Hector Vucetich here. During the nucleosynthesis, the most famous dimensionless parameters of the Standard Model could not differ from their present values more than by 10 percent.
Contrarians: constants evolve
OK, I have certainly omitted important teams that also argue that the evolution is zero. Let us hear the other side - which I will call the contrarians. Murphy, Webb, and Flambaum have measured some quasars differently in 2004, and they argued that the result for the relative change per year is
- 6 x 10^{-16} per year.
This is six ties higher than the upper limits found by the physicists mentioned at the beginning. Technically, however, the paper by Murphy, Webb, and Flambaum is twice as famous as the papers at the beginning that confirmed the null hypothesis. Right, I would naturally argue that this is probably due to the publication bias because people, especially in the field waiting for some new shocking things, simply prefer exciting news. It's more interesting to cite people who find 15-meter tall humans rather than those who say that the upper limit for height is around 3 meters. Giants bring you grants, and moreover you can stand on their toes (or shoulders, whichever you prefer).
I will prefer my theoretical preconceptions and continue to believe that the time evolution of the dimensionless numbers characteristic for the Standard Model is probably non-existent.
