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

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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 α=e²/(ℏ c) and the proton-to-electron mass ratio μ=mₚ/mₑ reveal no statistically significant variation over the last 90% of the lifetime of the Universe. At the 2σsignificance level, the following upper bounds are obtained for the epoch corresponding to the cosmological redshifts z 3 (i.e., 10 Gyr ago): |Δα/α| < 0.00016 and |Δμ/μ| < 0.00022. The corresponding upper limits to the time-average rates of the constant variations are |dα/(αdt)| < 1.6× 10⁻¹⁴ yr⁻¹ and |dμ/(μdt)| < 2.2×10⁻¹⁴ yr⁻¹. These limits serve as criteria for selection of those theoretical models which predict αand μvariation 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 αvalues in causally disconnected areas of the Universe.