Testing cosmological variations of fundamental physical constants by analysis of quasar spectra

Contemporary multidimensional cosmological theories predict different variations of fundamental physical constants in course of the cosmological evolution. On the basis of the QSO spectra analysis, we show that the fine-structure constant \alpha=e^2/(\hbar c) and the proton-to-electron mass ratio \mu=m_p/m_e reveal no statistically significant variation over the last 90% of the lifetime of the Universe. At the 2\sigma significance level, the following upper bounds are obtained for the epoch corresponding to the cosmological redshifts z ~ 3 (i.e., ~ 10 Gyr ago): |\Delta\alpha/\alpha| < 0.00016 and |\Delta\mu/\mu| < 0.00022. The corresponding upper limits to the time-average rates of the constant variations are |d\alpha/(\alpha dt)| < 1.6\times 10^{-14} yr^{-1} and |d\mu/(\mu dt)| < 2.2\times10^{-14} yr^{-1}. These limits serve as criteria for selection of those theoretical models which predict \alpha and \mu variation with the cosmological time. In addition, we test a possible anisotropy of the high-redshift fine splitting over the celestial sphere, which might reveal a non-equality of \alpha values in causally disconnected areas of the Universe.