We consider dark matter which has nonzero 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 $m_{\chi }>\mathcal{O}(\mathrm{MeV})$ and put constraints on their mass and electromagnetic couplings from cosmic microwave background (CMB) and large scale structure (LSS) observations. Fermionic dark matter with nonzero 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 baryon acoustic oscillations (BAO) observations. We find upper bounds on anapole moment $g_A<7.163\times {10}^3{\mathrm{GeV}}^{-2}$, electric dipole moment $\mathcal{D}<7.978\times {10}^{-9}e\mathrm{cm}$, magnetic dipole moment $\mu <2.959\times {10}^{-7}{\mu }_B$, and the bound on Rayleigh form factor of dark matter is $g_4/{\mathrm{\Lambda }}_4^2<1.085\times {10}^{-2}{\mathrm{GeV}}^{-2}$ with 95% C.L.

• Received 19 February 2021
• Accepted 22 June 2021

DOI:https://doi.org/10.1103/PhysRevD.104.023519

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Published by the American Physical Society