Constraints on electromagnetic form factors of sub-GeV dark matter from the cosmic microwave background anisotropy

We consider dark matter which have non-zero electromagnetic form factors like electric/magnetic dipole moments and anapole moment for fermionic dark matter and Rayleigh form factor for scalar dark matter. We consider dark matter mass $m_\chi > \cal{ O}({\rm MeV})$ and put constraints on their mass and electromagnetic couplings from CMB and LSS observations. Fermionic dark matter with non-zero electromagnetic form factors can annihilate to $e^+ e^-$ and scalar dark matter can annihilate to $2\gamma$ at the time of recombination and distort the CMB. We analyze dark matter with multipole moments with Planck and BAO observations. We find upper bounds on anapole moment $g_{A}<7.163\times 10^{3} …