Context :

Aims : To obtain limits on the variation of the fine-structure constant \alpha and the electron-to-proton mass ratio \mu over different cosmological epochs .

Methods : A new approach based on the comparison of redshifts of far infrared ( FIR ) fine-structure lines and low-lying rotational transitions in CO is proposed which is in principle more sensitive by a factor of \sim 10 compared to QSO metal absorption lines .

Results : Estimations of the quotient F = \alpha ^ { 2 } / \mu obtained for two distant quasars J1148+5251 ( z = 6.42 ) and BR 1202–0725 ( z = 4.69 ) provide { \Delta F } / { F } = ( 0.1 \pm 1.0 ) \times 10 ^ { -4 } and ( 1.4 \pm 1.5 ) \times 10 ^ { -4 } , respectively .
The obtained limits are consistent with no variation of physical constants at the level of \sim 0.01 % over a period of 13 Gyr .

Conclusions : Upcoming observations of quasars and distant galaxies in FIR fine-structure lines of different species and in CO low rotational lines at the SOFIA , HSO , and ALMA are expected to improve the current limit by , at least , an order of magnitude .