We consider dark matter particles as singlet fermionic particles carrying magnetic dipole moment to explore its contribution on the polarization of the cosmic microwave background (CMB) photons. We show that Dirac fermionic dark matter particles have no contribution on the CMB polarization. However, in the case of Majorana dark matter, this type of interaction leads to the B-mode polarization in the presence of primordial scalar perturbations which is in contrast with the standard scenario for the CMB polarization. We numerically calculate the B-mode power spectra and plot $$C_l^{BB}$$ClBB for different dark matter masses and the r-parameter. We show that dark matter particles with masses less than 100 MeV have a valuable contribution on $$C_l^{BB}$$ClBB. Meanwhile, dark matter particles with mass $$\text {m}_{\text {DM}}\le 50\, \text {MeV}$$mDM≤50MeV for $$r=0.07$$r=0.07 ( $$\text {m}_{\text {DM}}\le 80\, \text {MeV}$$mDM≤80MeV for $$r=0.09$$r=0.09) can be excluded experimentally. Furthermore, our results put a bound on the magnetic dipole moment about $$\text {M}\le 10^{-16} e\,\, \text {cm}$$M≤10-16ecm in agreement with the other reported constraints.

We consider a vector dark matter (VDM) with a direct coupling with photon. We examine the effect of such an interaction on the CMB polarization to put new constrains on the properties of the DM particles. We show that a partially polarized VDM of the order of temperature fluctuation with a quadrupole distribution leads to a valuable CP for the CMB. In different DM-models the DM-masses range from few eV to a few T eV . We show that the CP angular power spectrum depends on the mass of VDM as C (S) V l ∝ 1/m 6 V such that for m V = 10eV − 1keV , the CP angular power spectrum is C (S) V l ≃ 10 3 − 10 −11 nK 2 . Therefore, the light VDM with masses less than 10eV leads to an unexpected very large CP which can be excluded from the acceptable range of the VDM masses. 1