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.
Categories: astro-ph.CO