Testing cosmological variability of fundamental constants

One of the topical problems of contemporary physics is a possible variability of the fundamental constants. Here we consider possible variability of two dimensionless constants which are most important for calculation of atomic and molecular spectra (in particular, the X-ray ones): the fine-structure constant \alpha=e^2/\hbar c and the proton-to-electron mass ratio \mu=m_p/m_e. Values of the physical constants in the early epochs are estimated directly from observations of quasars - the most powerful sources of radiation, whose spectra were formed when the Universe was several times younger than now. A critical analysis of the available results leads to the conclusion that present-day data do not reveal any statistically significant evidence for variations of the fundamental constants under study. The most reliable upper limits to possible variation rates at the 95% confidence level, obtained in our work, read: |\dot\alpha/\alpha| < (1.4e-14)/yr, |\dot\mu/\mu| < (1.5e-14)/yr on the average over the last ten billion years.