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 α=e²/ℏc and the proton-to-electron mass ratio μ=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 the 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: |α̇/α|<1.4×10^-14 yr^-1, |μ̇/μ|<1.5×10^-14 yr^- on the average over the last 10¹⁰ yr. .