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

We investigate constraints on the time variation of the fine structure constant between the recombination epoch and the present epoch, Δα/α\equiv (α_{rec} - α_{now})/α_{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 Λ_{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 Δα/αis found to be -8.28 \times 10^{-3} < Δα/α< 1.81 \times 10^{-3}, which is tighter than the one obtained by considering only the change of αand m_{e}. We also obtain the constraint on the time variation of the proton-to-electron mass ratio μ\equiv m_{p}/m_{e} to be -0.52 < Δμ/μ< 0.17 (95% C.L.) under the same assumption. Finally, we also implement a forecast for constraints from the PLANCK survey.

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