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We consider dark matter as singlet fermionic particles which carrying magnetic dipole moment to explore its contribution on the polarization of cosmic microwave background (CMB) photons. We show that Dirac fermionic dark matter has 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 presence of primordial scalar perturbations which is in contrast with standard scenario for the CMB polarization. We numerically calculate the B-mode power spectra and plot C BB l for different dark matter masses and the r-parameter. We show that the dark matter with masses less than 100MeV have valuable contribution on C BB l . Meanwhile, the dark matters with mass m d ≤ 50M eV for r = 0.07 ( m d ≤ 80M eV for r = 0.09) can be excluded experimentally. Furthermore, our results put a bound on the magnetic dipole moment about M ≤ 10 −16 e cm in agreement with the other reported constraints.

A new model of the regular black hole in dimensions is introduced by considering an appropriate matter field as the energy‐momentum tensor. First, we propose a novel model of d‐dimensional energy density that in dimensions leads to the existence of an upper bound on the radius of the event horizon and a lower bound on the mass of the black hole which are motivated by the features of astrophysical black holes. According to these bounds, we introduce an admissible domain for the event horizon radius, depending on the metric parameters. After investigation of geometric properties of the obtained solutions, we study the thermal stability of the solution in the canonical ensemble and find that the regular black hole is thermally stable in the mentioned admissible domain. Besides, the free energy is calculated to examine the global stability of the solution.

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.