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If the seed magnetic fields exist in the early Universe, tensor components oftheir anisotropic stresses are not compensated prior to neutrino decoupling andthe tensor metric perturbations generated from them survive passively.Consequently, due to the decay of these metric perturbations afterrecombination, the so-called integrated Sachs-Wolfe effect, the large-scalefluctuations of CMB radiation are significantly boosted. This kind of CMBanisotropy is called the "tensor passive mode." Because these fluctuationsdeviate largely from the Gaussian statistics due to the quadratic dependence onthe strength of the Gaussian magnetic field, not only the power spectrum butalso the higher-order correlations have reasonable signals. With these motives,we compute the CMB bispectrum induced by this mode. When the magnetic spectrumobeys a nearly scale-invariant shape, we obtain an estimation of a typicalvalue of the normalized reduced bispectrum as $\ell_1(\ell_1 +1)\ell_3(\ell_3+1)|b_{\ell_1\ell_2\ell_3}| \sim (130-6) \times 10^{-16} (B_{1\rm Mpc} / 4.7 {\rm nG})^6$ depending on the energy scale of the magnetic fieldproduction from $10^{14}$GeV to $10^3$GeV. Here, $B_{1 {\rm Mpc}}$ is thestrength of the primordial magnetic field smoothed on $1 {\rm Mpc}$. From theabove estimation and the current observational constraint on the primordialnon-Gaussianity, we get a rough constraint on the magnetic field strength as$B_{1 {\rm Mpc}} < 2.6 - 4.4 {\rm nG}$.

Cosmic microwave background bispectrum of tensor passive modes induced from primordial magnetic fields