Effects of electrically charged dark matter on cosmic microwave background anisotropies

We examine the possibility that dark matter consists of charged massive particles (CHAMPs) in view of the cosmic microwave background (CMB) anisotropies. The evolution of cosmological perturbations of CHAMPs with other components is followed in a self-consistent manner, without assuming that CHAMPs and baryons are tightly coupled. We incorporate for the first time the “kinetic recoupling” of the Coulomb scattering, which is characteristic of heavy CHAMPs. By a direct comparison of the predicted CMB temperature/polarization autocorrelations in CHAMP models and the observed spectra in the Planck mission, we show that CHAMPs leave sizable effects on them if it is lighter than $10^{11}\mathrm{GeV}$. Our result can be applicable to any CHAMP as long as its lifetime is much longer than the cosmic time at the recombination ($\sim 4\times 10^5\mathrm{yr}$). An application to millicharged particles is also discussed.

Figure 1

Evolution of $\gamma /H$ with the scale factor ($a$ normalized such that $a=1$ at present). The cosmic time goes from left to right. We take $m_{\text{Ch}}=10^8$, $10^9$, $10^{10}$, $10^{11}$, and $10^{12}\mathrm{GeV}$. It can be scaled to any CHAMP mass by $\gamma \propto 1/m_{\text{Ch}}$ We show the Gamow criterion ($\gamma /H=1$) for reference.

Figure 2

Linear matter power spectra at present in the CHAMP models with $m_{\text{Ch}}=10^{10}$, $10^{11}$, and $10^{12}\mathrm{GeV}$. In the top panel, we also show the spectrum in the standard CDM models, where DM particles do not have any interaction other than the gravitational one. We compare the differences between the CHAMP models and the standard CDM model in the bottom panel. The heavier CHAMP model ($m_{\text{Ch}}=10^{12}\mathrm{GeV}$) is quite close to the standard CDM model at larger length scales ($k\ll 10^{3}h/\mathrm{Mpc}$).

Figure 3

The same as in the bottom panel of Fig. 2, but zooming in on the baryon acoustic oscillations. We also show the relative errors in the BOSS DR11 data (“post-recon”) [46] for reference. Note that the vertical offset may be compensated by a choice of the template model parameters such as a galaxy bias, which are varied when the template model is fit to the data (see Ref. [46] for details).

Figure 4

CMB $TT$ power spectra in the CHAMP models with $m_{\text{Ch}}=10^{10}$, $10^{11}$, and $10^{12}\mathrm{GeV}$. We also show the spectrum in the standard CDM model. Squares with error bars represent the observed spectrum in Planck 2015. The heavier CHAMP models ($m_{\text{Ch}}=10^{11}$ and $10^{12}\mathrm{GeV}$) are quite close to the standard CDM model. We adopt the cosmological parameters listed as “Planck $\mathrm{TT}+\mathrm{lowP}$” in Ref. [43].

Figure 5

The same as in Fig. 4, but for CMB $EE$ power spectra. The heavier CHAMP model ($m_{\text{Ch}}=10^{12}\mathrm{GeV}$) is quite close to the standard CDM model.

Figure 6

Summary of constraints on millicharged particles in the mass–charge plane. The direct detection constraint like the Large Underground Xenon (LUX) experiment [49] puts an upper bound on the charge, while millicharged particles with a larger charge lose their energy in the atmosphere [2] and thus are not subject to the constraint. In summary, the direct detection constraint excludes only the shaded region. The Galactic magnetic field may reduce the number density of millicharged particles in the Galactic disk to open a larger window [6]. It may also relax the severe constraints from a search of heavy isotopes in deep sea water [2, 5] and cosmic-ray detectors (Pioneer 11) [2]. These two constraints and that from the CBBN [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20] are originally given in CHAMP models, and their extensions to millicharged particles are nontrivial. Hence, we show their constraints just on the axis of $\epsilon =1$. Millicharged particles lose their energy through the scattering with electrons in the hot-ionized component of the disk interstellar medium and may not maintain a halo [2]. A severe constraint is suggested from the observation that a random walk of millicharged massive particles in the galaxy cluster magnetic field may smear the DM profile [7]. The constraints are applicable if millicharged particles are (quasi)stable over the age of the Universe (${\tau }_{\text{Ch}}\gtrsim 10^{10}\mathrm{yr}$) unless denoted explicitly. The constraints from the CBBN and the CMB anisotropies (this work) are applicable even if millicharged particles are unstable (${\tau }_{\text{Ch}}\gtrsim 30\mathrm{hr}$ and $4\times 10^5\mathrm{yr}$, repsectively), but its mass density before the decay is identical to that of DM.