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While the behavior of the dominant component of the dark matter is reasonablywell established by cosmological observables, its particle nature andinteractions with the rest of the matter are not known. We consider three darkmatter models that admit electromagnetic interaction between baryons and darkmatter: (a) milli-charged particle (CCDM) of charge $q_{\rm ccdm}$ and mass$m_{\rm ccdm}$, (b) a neutral atom of two charged particles of mass $m_{\rmdd}$ (DD), and (c) a neutral atom of doubly charged particle and helium nucleus(HeD). We derive and discuss in detail the formation, stability, andinteraction of these atoms with baryons. We derive the implications of this newinteraction in the tight-coupling approximation, which allows us toanalytically gauge their impact on the matter power spectrum and CMBanisotropy. We incorporate this new interaction into the publicly-availablecode CLASS to obtain numerical results. We compare our results with Planck 2018data to constrain the fraction of interacting dark matter. For the range ofallowed astrophysical parameters, the HeD atom yields the results of$\Lambda$CDM model for $k < 1 \, \rm Mpc^{-1}$, and hence its fraction is notconstrained by CMB anisotropy data which is sensitive to $k < 0.2 \, \rmMpc^{-1}$. For $m_{\rm dd} \gtrsim 25 \, \rm GeV$, the DD atom is also notconstrained by CMB data. For $m_{\rm dd} = 10 \, \rm GeV$, the CMB dataconstrains the fraction of DD atoms to be smaller than 4% of the total CDMcomponent. For $q_{\rm ccdm} = 10^{-6}e$ and $m_{\rm ccdm} = 50 \, \rm MeV$,the CCDM fraction is constrained to be less than 1%.

journal of cosmology and astroparticle physics

Cosmological implications of electromagnetically interacting dark  matter: milli-charged particles and atoms with singly and doubly charged dark  matter