Does the proton-to-electron mass ratio vary in the course of cosmological evolution?

The possible cosmological variation of the proton-to-electron mass ratio was estimated by measuring the H_2 wavelengths in the high-resolution spectrum of the quasar Q~0347-382. Our analysis yielded an estimate for the possible deviation of \mu value in the past, 10 Gyr ago: for the unweighted value $\mathrm{\Delta }\mu \mathrm{/}\mu =(3.0\pm 2.4)\times {10}^{-5}$; for the weighted value $$\mathrm{\Delta }\mu \mathrm{/}\mu =(5.02\pm 1.82)\times {10}^{-5}$$ Since the significance of the both results does not exceed 3$\sigma$, further observations are needed to increase the statistical significance. In any case, this result may be considered as the most stringent estimate on an upper limit of a possible variation of \mu (95% C.L.): $$\mathrm{\mid }\mathrm{\Delta }\mu \mathrm{/}\mu \mathrm{\mid }<8\times {10}^{-5}$$ This value serves as an effective tool for selection of models determining a relation between possible cosmological deviations of the fine-structure constant \alpha and the elementary particle masses (m${}_p$, m${}_e$, etc.).