Constraining the time variation of the coupling constants from cosmic microwave background: effect of \Lambda_{QCD}

We investigate constraints on the time variation of the fine structure constant between the recombination epoch and the present epoch, \Delta\alpha/\alpha \equiv (\alpha_{rec} - \alpha_{now})/\alpha_{now}, from cosmic microwave background (CMB) taking into account simultaneous variation of other physical constants, namely the electron mass m_{e} and the proton mass m_{p}. In other words, we consider the variation of Yukawa coupling and the QCD scale \Lambda_{QCD} in addition to the electromagnetic coupling. We clarify which parameters can be determined from CMB temperature anisotropy in terms of singular value decomposition. Assuming a relation among variations of coupling constants governed by a single scalar field (the dilaton), the 95% confidence level (C.L.) constraint on \Delta\alpha/\alpha is found to be -8.28 \times 10^{-3} < \Delta\alpha/\alpha < 1.81 \times 10^{-3}, which is tighter than the one obtained by considering only the change of \alpha and m_{e}. We also obtain the constraint on the time variation of the proton-to-electron mass ratio \mu \equiv m_{p}/m_{e} to be -0.52 < \Delta\mu/\mu < 0.17 (95% C.L.) under the same assumption. Finally, we also implement a forecast for constraints from the PLANCK survey.