Exploring Dark Forces with Multimessenger Studies of Extreme Mass Ratio Inspirals

The exploration of dark sector interactions via gravitational waves (GWs) from binary inspirals has been a subject of recent interest. We study dark forces using extreme mass ratio inspirals (EMRIs), pointing out two issues of interest. Firstly, the innermost stable circular orbit (ISCO) of the EMRI, which sets the characteristic length scale of the system and hence the dark force range to which it exhibits enhanced sensitivity, probes force mediator masses that complement those studied with supermassive black hole (SMBH) or neutron star binaries. The LISA mission (the proposed $\mu$Ares detector) will probe mediators with masses $m_V \sim 10^{-16}~{\rm eV}$ ($m_V \sim 10^{-18}~{\rm eV}$), corresponding to ISCOs of $10^6 M_\odot$ ($10^8 M_\odot$) central SMBHs. Secondly, while the sensitivity to dark couplings is typically limited by the uncertainty in the binary component masses, independent mass measurements of the central SMBH through reverberation mapping campaigns or the motion of dynamical tracers enable one to break this degeneracy. Our results, therefore, highlight the necessity for coordinated studies, loosely referred to as "multimessenger", between future $\mu{\rm Hz}-{\rm mHz}$ GW observatories and ongoing and forthcoming SMBH mass measurement campaigns, including OzDES-RM, SDSS-RM, and SDSS-V Black Hole Mapper.