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

The possible cosmological variation of the proton-to-electron mass ratio mu = m(p)/m(e) was estimated by measuring the H-2 wavelengths in the spectra of distant quasars. We analyze high-resolution (FWHM approximate to 7 km s(-1)) spectra of the two damped Lyman-alpha 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 mu in the past similar to10 Gyr, Deltamu/mu = (5.7 +/- 3.8) x 10(-5). Since the significance of this result does not exceed 1.5sigma, further observations are needed to increase the statistical significance. This is the most stringent limit on the possible cosmological variation of la to date. (C) 2002 MAIK "Nauka/Interperiodica".