- Access by Xinjiang University
CMB limits on the absorption of light vector and axial-vector dark matter
Phys. Rev. D 114, 023548 – Published 22 July, 2026
DOI: https://doi.org/10.1103/nkk2-k7f9
Abstract
Leptophilic sub-MeV spin-1 dark matter (DM) can be converted into a photon via inelastic scattering with a free electron or absorption by a neutral hydrogen atom in the primordial plasma. We study for the first time the impact of the energy injection resulting from such processes on cosmic microwave background (CMB) anisotropies. We obtain upper limits on the vector and axial-vector DM-electron couplings using Planck 2018 temperature, polarization, and lensing data for DM masses between 100 eV and 100 keV. We find that, due to the suppression of the hydrogen atomic form factor at high energies, inelastic scattering provides the dominant constraint for DM masses above the keV scale. At lower masses, hydrogen ionization through DM absorption is the leading channel, driven by the higher efficiency of postrecombination energy injection in modifying the free-electron fraction. Although the bounds we derive are considerably weaker than existing laboratory and astrophysical limits, they provide a robust and independent cosmological probe of leptophilic DM interactions.
Physics Subject Headings (PhySH)
Article Text
References (99)
- J. A. Adams, S. Sarkar, and D. W. Sciama, CMB anisotropy in the decaying neutrino cosmology, Mon. Not. R. Astron. Soc. 301, 210 (1998).
- X.-L. Chen and M. Kamionkowski, Particle decays during the cosmic dark ages, Phys. Rev. D 70, 043502 (2004).
- N. Padmanabhan and D. P. Finkbeiner, Detecting dark matter annihilation with CMB polarization: Signatures and experimental prospects, Phys. Rev. D 72, 023508 (2005).
- L. Zhang, X.-L. Chen, Y.-A. Lei, and Z.-G. Si, The impacts of dark matter particle annihilation on recombination and the anisotropies of the cosmic microwave background, Phys. Rev. D 74, 103519 (2006).
- L. Zhang, X. Chen, M. Kamionkowski, Z.-g. Si, and Z. Zheng, Constraints on radiative dark-matter decay from the cosmic microwave background, Phys. Rev. D 76, 061301 (2007).
- S. Galli, F. Iocco, G. Bertone, and A. Melchiorri, CMB constraints on dark matter models with large annihilation cross-section, Phys. Rev. D 80, 023505 (2009).
- T. R. Slatyer, N. Padmanabhan, and D. P. Finkbeiner, CMB constraints on WIMP annihilation: Energy absorption during the recombination epoch, Phys. Rev. D 80, 043526 (2009).
- T. Kanzaki, M. Kawasaki, and K. Nakayama, Effects of dark matter annihilation on the cosmic microwave background, Prog. Theor. Phys. 123, 853 (2010).
- G. Hutsi, J. Chluba, A. Hektor, and M. Raidal, WMAP7 and future CMB constraints on annihilating dark matter: Implications on GeV-scale WIMPs, Astron. Astrophys. 535, A26 (2011).
- S. Galli, F. Iocco, G. Bertone, and A. Melchiorri, Updated CMB constraints on dark matter annihilation cross sections, Phys. Rev. D 84, 027302 (2011).
- G. Giesen, J. Lesgourgues, B. Audren, and Y. Ali-Haimoud, CMB photons shedding light on dark matter, J. Cosmol. Astropart. Phys. 12 (2012) 008.
- D. P. Finkbeiner, S. Galli, T. Lin, and T. R. Slatyer, Searching for dark matter in the CMB: A compact parametrization of energy injection from new physics, Phys. Rev. D 85, 043522 (2012).
- T. R. Slatyer, Energy injection and absorption in the cosmic dark ages, Phys. Rev. D 87, 123513 (2013).
- J. M. Cline and P. Scott, Dark matter CMB constraints and likelihoods for poor particle physicists, J. Cosmol. Astropart. Phys. 03 (2013) 044; 05 (2013) E01.
- C. Weniger, P. D. Serpico, F. Iocco, and G. Bertone, CMB bounds on dark matter annihilation: Nucleon energy-losses after recombination, Phys. Rev. D 87, 123008 (2013).
- L. Lopez-Honorez, O. Mena, S. Palomares-Ruiz, and A. C. Vincent, Constraints on dark matter annihilation from CMB observationsbefore Planck, J. Cosmol. Astropart. Phys. 07 (2013) 046.
- R. Diamanti, L. Lopez-Honorez, O. Mena, S. Palomares-Ruiz, and A. C. Vincent, Constraining dark matter late-time energy injection: Decays and P-Wave annihilations, J. Cosmol. Astropart. Phys. 02 (2013) 017.
- M. S. Madhavacheril, N. Sehgal, and T. R. Slatyer, Current dark matter annihilation constraints from CMB and low-redshift data, Phys. Rev. D 89, 103508 (2014).
- S. Galli, T. R. Slatyer, M. Valdes, and F. Iocco, Systematic uncertainties in constraining dark matter annihilation from the cosmic microwave background, Phys. Rev. D 88, 063502 (2013).
- T. R. Slatyer, Indirect dark matter signatures in the cosmic dark ages. I. Generalizing the bound on s-wave dark matter annihilation from Planck results, Phys. Rev. D 93, 023527 (2016).
- V. Poulin, P. D. Serpico, and J. Lesgourgues, A fresh look at linear cosmological constraints on a decaying dark matter component, J. Cosmol. Astropart. Phys. 08 (2016) 036.
- T. R. Slatyer and C.-L. Wu, General constraints on dark matter decay from the cosmic microwave background, Phys. Rev. D 95, 023010 (2017).
- H. Liu, T. R. Slatyer, and J. Zavala, Contributions to cosmic reionization from dark matter annihilation and decay, Phys. Rev. D 94, 063507 (2016).
- V. Poulin, J. Lesgourgues, and P. D. Serpico, Cosmological constraints on exotic injection of electromagnetic energy, J. Cosmol. Astropart. Phys. 03 (2016) 043.
- J. Cang, Y. Gao, and Y.-Z. Ma, Probing dark matter with future CMB measurements, Phys. Rev. D 102, 103005 (2020).
- M. Kawasaki, H. Nakatsuka, K. Nakayama, and T. Sekiguchi, Revisiting CMB constraints on dark matter annihilation, J. Cosmol. Astropart. Phys. 12 (2021) 015.
- H. Liu, W. Qin, G. W. Ridgway, and T. R. Slatyer, Exotic energy injection in the early universe. II. CMB spectral distortions and constraints on light dark matter, Phys. Rev. D 108, 043531 (2023).
- F. Capozzi, R. Z. Ferreira, L. Lopez-Honorez, and O. Mena, CMB and Lyman- constraints on dark matter decays to photons, J. Cosmol. Astropart. Phys. 06 (2023) 060.
- C. Xu, W. Qin, and T. R. Slatyer, CMB limits on decaying dark matter beyond the ionization threshold, Phys. Rev. D 110, 123529 (2024).
- G. Montefalcone, G. Elor, K. K. Boddy, and N. Bellomo, CMB constraints on loop-induced decays of leptophilic dark matter, Phys. Rev. D 112, 023506 (2025).
- R. Essig et al., Working group report: New light weakly coupled particles, in Snowmass 2013: Snowmass on the Mississippi (2013), arXiv:1311.0029.
- J. Alexander et al., Dark sectors 2016 Workshop: Community report, arXiv:1608.08632.
- M. Fabbrichesi, E. Gabrielli, and G. Lanfranchi, The dark photon, arXiv:2005.01515.
- A. Caputo and R. Essig, The dark photon: A 2026 perspective, arXiv:2603.08430.
- D. J. H. Chung, E. W. Kolb, and A. Riotto, Nonthermal supermassive dark matter, Phys. Rev. Lett. 81, 4048 (1998).
- A. Ahmed, B. Grzadkowski, and A. Socha, Gravitational production of vector dark matter, J. High Energy Phys. 08 (2020) 059.
- E. W. Kolb and A. J. Long, Cosmological gravitational particle production and its implications for cosmological relics, Rev. Mod. Phys. 96, 045005 (2024).
- A. E. Nelson and J. Scholtz, Dark light, dark matter and the misalignment mechanism, Phys. Rev. D 84, 103501 (2011).
- P. Agrawal, N. Kitajima, M. Reece, T. Sekiguchi, and F. Takahashi, Relic abundance of dark photon dark matter, Phys. Lett. B 801, 135136 (2020).
- C. Boehm, T. A. Ensslin, and J. Silk, Can annihilating dark matter be lighter than a few GeVs?, J. Phys. G 30, 279 (2004).
- P. D. Serpico and G. G. Raffelt, MeV-mass dark matter and primordial nucleosynthesis, Phys. Rev. D 70, 043526 (2004).
- K. M. Nollett and G. Steigman, BBN and the CMB constrain light, electromagnetically coupled WIMPs, Phys. Rev. D 89, 083508 (2014).
- G. Steigman and K. M. Nollett, Light WIMPs, equivalent neutrinos, BBN, and the CMB, Mem. Soc. Astron. Ital. 85, 175 (2014).
- K. M. Nollett and G. Steigman, BBN and the CMB constrain neutrino coupled light WIMPs, Phys. Rev. D 91, 083505 (2015).
- M. Escudero, Neutrino decoupling beyond the standard model: CMB constraints on the dark matter mass with a fast and precise evaluation, J. Cosmol. Astropart. Phys. 02 (2018) 007.
- N. Sabti, J. Alvey, M. Escudero, M. Fairbairn, and D. Blas, Refined bounds on MeV-scale thermal dark sectors from BBN and the CMB, J. Cosmol. Astropart. Phys. 01 (2019) 004.
- C. Giovanetti, M. Lisanti, H. Liu, and J. T. Ruderman, Joint cosmic microwave background and big bang nucleosynthesis constraints on light dark sectors with dark radiation, Phys. Rev. Lett. 129, 021302 (2022).
- R. An, K. K. Boddy, and V. Gluscevic, Interacting light thermal-relic dark matter: Self-consistent cosmological bounds, Phys. Rev. D 109, 123522 (2024).
- N. Aghanim et al. (Planck Collaboration), Planck 2018 results. V. CMB power spectra and likelihoods, Astron. Astrophys. 641, A5 (2020).
- H. Liu, G. W. Ridgway, and T. R. Slatyer, Code package for calculating modified cosmic ionization and thermal histories with dark matter and other exotic energy injections, Phys. Rev. D 101, 023530 (2020).
- H. Liu, W. Qin, G. W. Ridgway, and T. R. Slatyer, Exotic energy injection in the early universe. I. A novel treatment for low-energy electrons and photons, Phys. Rev. D 108, 043530 (2023).
- D. Blas, J. Lesgourgues, and T. Tram, The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes, J. Cosmol. Astropart. Phys. 07 (2011) 034.
- C. Baruch, P. Ilten, Y. Soreq, and M. Williams, Axial vectors in DarkCast, J. High Energy Phys. 11 (2022) 124.
- T. Cohen, D. E. Morrissey, and A. Pierce, Changes in dark matter properties after freeze-out, Phys. Rev. D 78, 111701 (2008).
- M. J. Baker, J. Kopp, and A. J. Long, Filtered dark matter at a first order phase transition, Phys. Rev. Lett. 125, 151102 (2020).
- G. Elor, R. McGehee, and A. Pierce, Maximizing direct detection with highly interactive particle relic dark matter, Phys. Rev. Lett. 130, 031803 (2023).
- A. Das, S. Das, and S. K. Sethi, Mass-varying dark matter and its cosmological signature, Phys. Rev. D 108, 083501 (2023).
- S. Mandal and N. Sehgal, Mass-varying dark matter from a phase transition, Phys. Rev. D 107, 123003 (2023).
- J. Redondo and M. Postma, Massive hidden photons as lukewarm dark matter, J. Cosmol. Astropart. Phys. 02 (2008) 005.
- E. Hardy and R. Lasenby, Stellar cooling bounds on new light particles: Plasma mixing effects, J. High Energy Phys. 02 (2016) 033.
- H. An, M. Pospelov, and J. Pradler, New stellar constraints on dark photons, Phys. Lett. B 725, 190 (2013).
- J. Redondo and G. Raffelt, Solar constraints on hidden photons re-visited, J. Cosmol. Astropart. Phys. 08 (2013) 034.
- S. Knapen, T. Lin, and K. M. Zurek, Light dark matter: Models and constraints, Phys. Rev. D 96, 115021 (2017).
- H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms, 1st ed. (Springer-Verlag, Berlin, 1957).
- I. I. Sobelman, Atomic Spectra and Radiative Transitions, 2nd ed. (Springer-Verlag, Berlin, 1992).
- P. Stöcker, M. Krämer, J. Lesgourgues, and V. Poulin, Exotic energy injection with ExoCLASS: Application to the Higgs portal model and evaporating black holes, J. Cosmol. Astropart. Phys. 03 (2018) 018.
- Y. Ali-Haïmoud, S. Seher Gandhi, and T. L. Smith, Exact treatment of weak dark matter-baryon scattering for linear-cosmology observables, Phys. Rev. D 109, 083523 (2024).
- B. Audren, J. Lesgourgues, K. Benabed, and S. Prunet, Conservative constraints on early cosmology: An illustration of the montepython cosmological parameter inference code, J. Cosmol. Astropart. Phys. 02 (2012) 001.
- T. Brinckmann and J. Lesgourgues, montepython 3: Boosted MCMC sampler and other features, Phys. Dark Universe 24, 100260 (2019).
- A. Gelman and D. Rubin, Inference from iterative simulation using multiple sequences, Stat. Sci. 7, 457 (1992).
- A. Lewis, getdist: A Python package for analysing Monte Carlo samples, arXiv:1910.13970.
- P. Agnes et al. (DarkSide Collaboration), Search for dark matter particle interactions with electron final states with DarkSide-50, Phys. Rev. Lett. 130, 101002 (2023).
- E. Aprile et al. (XENON Collaboration), Light dark matter search with ionization signals in XENON1T, Phys. Rev. Lett. 123, 251801 (2019).
- E. Aprile et al. (XENON Collaboration), Excess electronic recoil events in XENON1T, Phys. Rev. D 102, 072004 (2020).
- E. Aprile et al. (XENON Collaboration)§, XENON), Emission of single and few electrons in XENON1T and limits on light dark matter, Phys. Rev. D 106, 022001 (2022).
- E. Aprile et al. (XENON Collaboration), Search for new physics in electronic recoil data from XENONnT, Phys. Rev. Lett. 129, 161805 (2022).
- T. Aralis et al. (SuperCDMS Collaboration), Constraints on dark photons and axionlike particles from the SuperCDMS soudan experiment, Phys. Rev. D 101, 052008 (2020); 103, 039901(E) (2021).
- J. Redondo, Helioscope bounds on hidden sector photons, J. Cosmol. Astropart. Phys. 07 (2008) 008.
- R. Laha, J. B. Muñoz, and T. R. Slatyer, INTEGRAL constraints on primordial black holes and particle dark matter, Phys. Rev. D 101, 123514 (2020).
- R. Z. Ferreira, M. C. D. Marsh, and E. Müller, Do direct detection experiments constrain axionlike particles coupled to electrons?, Phys. Rev. Lett. 128, 221302 (2022).
- D. K. Hong, C. S. Shin, and S. Yun, Cooling of young neutron stars and dark gauge bosons, Phys. Rev. D 103, 123031 (2021).
- M. J. Dolan, F. J. Hiskens, and R. R. Volkas, Constraining dark photons with self-consistent simulations of globular cluster stars, J. Cosmol. Astropart. Phys. 05 (2023) 099.
- D. Croon, G. Elor, R. K. Leane, and S. D. McDermott, Supernova muons: New constraints on ’ bosons, axions and ALPs, J. High Energy Phys. 01 (2020) 107.
- F. Pérez and B. Granger, ipython: A system for interactive scientific computing, Comput. Sci. Eng. 9, 21 (2007).
- M. F. Gu, dielectronic recombination as a line formation process in photoionized plasmas, Astrophys. J. Lett. 579, L103 (2002).
- M. F. Gu, Indirect X-ray line-formation processes in iron L-shell ions, Astrophys. J. 582, 1241 (2003).
- M. F. Gu, The flexible atomic code, Can. J. Phys. 86, 675 (2008).
- R. Mertig, M. Bohm, and A. Denner, feyncalc: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64, 345 (1991).
- V. Shtabovenko, R. Mertig, and F. Orellana, New developments in feyncalc 9.0, Comput. Phys. Commun. 207, 432 (2016).
- V. Shtabovenko, R. Mertig, and F. Orellana, feyncalc 9.3: New features and improvements, Comput. Phys. Commun. 256, 107478 (2020).
- V. Shtabovenko, R. Mertig, and F. Orellana, feyncalc 10: Do multiloop integrals dream of computer codes?, Comput. Phys. Commun. 306, 109357 (2025).
- J. Hunter, matplotlib: A 2D graphics environment, Comput. Sci. Eng. 9, 90 (2007).
- C. Harris et al., Array programming with numpy, Nature (London) 585, 3572 (2020).
- P. Virtanen et al., scipy 1.0—fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).
- C. O’Hare, cajohare/axionlimits: Axionlimits, https://cajohare.github.io/AxionLimits/ (2020).
- A. Caputo, A. J. Millar, C. A. J. O’Hare, and E. Vitagliano, Dark photon limits: A handbook, Phys. Rev. D 104, 095029 (2021).
- M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, USA, 1995).
- H. B. T. Tan, A. Derevianko, V. A. Dzuba, and V. V. Flambaum, Atomic ionization by scalar dark matter and solar scalars, Phys. Rev. Lett. 127, 081301 (2021).
- M. Ibe, W. Nakano, Y. Shoji, and K. Suzuki, Migdal effect in dark matter direct detection experiments, J. High Energy Phys. 03 (2017) 194.