Dipolar dark matter and CMB B-mode polarization

Eur. Phys. J. C (2020) 80:402 https://doi.org/10.1140/epjc/s10052-020-7982-y Regular Article - Theoretical Physics Dipolar dark matter and CMB B-mode polarization S. Mahmoudi1,a , M. Haghighat1,2,b , S. Al. Modares Vamegh1,c , R. Mohammadi3,4,d 1 Physics Department, College of Sciences, Shiraz University, 71454 Shiraz, Iran 2 Islamic World Science Citation Center, 71946-94173 Shiraz, Iran 3 Iranian National Science and Technology Museum (INMOST), P.O. Box: 11369-14611, Tehran, Iran 4 School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran, Iran Received: 31 May 2018 / Accepted: 28 April 2020 © The Author(s) 2020 Abstract 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 ClB B 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 ClB B . Meanwhile, dark matter particles with mass mDM ≤ 50 MeV for r = 0.07 ( mDM ≤ 80 MeV 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. 1 Introduction The nature of dark matter (DM) and its interactions is one of the most important questions in cosmology and particle physics. Although there is some wealth of cosmological evidence for existing DM, from galactic clusters and velocity curves of spinning galaxies to gravitational lensing [1–8], its particle properties have remained elusive. To explore the nature of DM, different experiments have been proposed such as DAMA/LIBRA collaboration at Gran Sasso [9], CoGeNT collaboration at the Soudan Laboratory underground [10] and CDMS collaba e-mail: b e-mail: c e-mail: oration [11] which are introduced to detect DM directly. In these experiments, the scattering of DM from nucleons can be described by multiple interactions. In fact, DM particle has zero electric charge and therefore in the simplest extension of the standard model, it can be coupled to photon through an intrinsic electric and /or magnetic dipole moments which is well-known as dipolar DM (DDM) model [12–16]. However, the DDM model can successfully explain some claims of DAMA/LIBRA and COGENT collaborations [17,18]. The CMB photons are expected to be linearly polarized due to the anisotropic Compton scattering around the epoch of recombination. Meanwhile, according to the standard scenario of cosmology, there is no physical mechanism to generate circularly polarized radiation at the last scattering surface. However, studies conducted in recent years show that the interaction between photons and matter can convert or generate the polarization states of photons in different situations. For instance, the linear polarization of the CMB photons can be converted to the circular one in the presence of background fields or due to the effects of particle scattering which has been widely discussed in the literature [19–30]. In this paper, we consider the DDM model with a singlet spin 21 fermion as DM particles to examine the effects of magnetic dipole moments on the CMB photon polarization. Generally, the CMB polarization pattern has two geometrical components, E-mode and B-mode. These modes based on the Stokes parameters U and Q can form an independent local coordinate system [31–35]. According to the standard model of cosmology, while E-mode polarization of the CMB can be produced by Compton scattering at the last scattering surface in the presence of scalar and tensor perturbations, its B-mode polarization pattern can only be produced at the presence of tensor perturbations. Nevertheless, it has been shown that it is also possible to produce B-mode d e-mail: (corresponding author) 0123456789().: V,-vol 123 402 Page 2 of 13 polarization in the presence of scalar perturbations. Since the detection of the B-mode polarization can provide a unique tool to investigate the CMB perturbations, it is important to identify all potential sources of the B-mode polarization. As the new sources, for instance, in [36] the effect of the Faraday rotation due to the uniform magnetic field on the CMB is investigated and it is shown that a nonvanishing Bmode polarization can be produced through Faraday rotation. In [37,38], the authors have discussed that photon-neutrino interaction in the presence of scalar perturbations could be considered as one of the sources of the CMB B-mode polarization. It is also shown that the Compton scattering in the non-commutative space-time can generate the B-mode polarization of the CMB [39] and the possibility of the producing B-mode polarization pattern due to polarized Compton scattering in the presence of scalar perturbations has been discussed in [40]. However, the parameter which characterizes the amplitude of the metric tensor perturbation is r = PT /PS where PT = A T (k/k◦ )n T −1 and PS = A S (k/k◦ )n S −1 are, respectively, the power spectra of tensor and scalar metric perturbations and n T,S and A T,S are their spectral indices and amplitudes. The r parameter is usually calculated by comparing the B-mode and E-mode power spectra. Recent measurements of BICEP2 + Keck Array + Planck (BKP) report an upper bound r0.002 < 0.09 [41]. In this work, we will show that the magnetic like component of the CMB polarization (B-mode polarization) can be produced by the photon-DM interaction in the presence of scalar perturbations. The paper is organized as follows: we introduce the effective Lagrangian for the interaction of DDM with photons in Sect. 2. Then we give a brief introduction to the Stokes parameters and drive the time evolution of these parameters in terms of the photon-DM scattering in Sect. 3. The power spectrum is evaluated numerically in Sect. 4. We compare our results with the experimental data and give some discussion in Sect. 5. 2 Dipolar dark matter model A particle as a candidate for DM is generally known as a stable or relatively stable particle that does not interact electromagnetically. However, in recent years, there are some interests in the study of the electromagnetic interactions of DM. Such a particle has not probably the electric charge otherwise it has significant interaction with the photons and could be easily detected. But this particle can weakly couple with the electromagnetic field through loop corrections. The most general form for the electromagnetic current between fermions consis (...truncated)