Do the fundamental constants vary in the course of cosmological evolution?

The possible cosmological variation of the proton-to-electron mass ratio μ = m _p/m _e was estimated by measuring the H₂ wavelengths in the spectra of distant quasars. We analyze high-resolution (FWHM≈7 km s^?1) spectra of the two damped Lyman-α systems at redshifts z _abs=2.3377 and 3.0249 observed in the spectra of the quasars Q 1232+082 and Q 0347?382, respectively. Our analysis yielded the most conservative estimate for the possible variation of μ in the past ～ 10 Gyr, Δμ/μ = (5.7 ± 3.8) × 10^?5. Since the significance of this result does not exceed 1.5σ, further observations are needed to increase the statistical significance. This is the most stringent limit on the possible cosmological variation of μ to date.