Endeavours of the unification of the four fundamental interactions have resulted in a development of theories having cosmological solutions in which low-energy limits of fundamental physical constants vary with time. The validity of such theoretical models should be checked by comparison of the theoretical predictions with observational and experimental bounds on possible time-dependences of the fundamental constants.
Based on high-resolution measurements of quasar spectra, we obtain
the following direct limits on the average rate of the cosmological
time variation of the fine-structure constant alpha:
|alpha'/alpha| < 3.1 10^-14 yr-1
It is the most conservative limit.
Here we analyze a new, high-resolution spectrum of the z=2.81080
molecular hydrogen absorption system toward the QSO PKS 0528-250
to derive a new observational constraint to the time-averaged variation
rate of the proton-to-electron mass ratio. We find
|mu'/mu| < 1.5 10-14 yr-1
which is much tighter than previously measured limits.
Analogous estimates published previously, as well as other contemporary tests for possible variations of alpha and mu (those based on the "Oklo phenomenon", on the primordial nucleosynthesis models, and others) are discussed and compared with the present upper limits. We argue that the present results are the most conservative one.