Gravitational-wave cosmology with extreme mass-ratio inspirals

The Laser Interferometer Space Antenna (LISA) will open the mHz frequency window of the gravitational-wave (GW) landscape. Among all the new GW sources expected to emit in this frequency band, extreme mass-ratio inspirals (EMRIs) constitute a unique laboratory for astrophysics and fundamental physics. Here, we show that EMRIs can also be used to extract relevant cosmological information, complementary to both electromagnetic (EM) and other GW observations. By using the loudest EMRIs (S/N > 100) detected by LISA as dark standard sirens, statistically matching their sky localization region with mock galaxy catalogues, we find that constraints on H0 can reach ∼1.1 per cent (∼3.6 per cent) accuracy, at the 90 per cent credible level, in our best(worst)- case scenario. By considering a dynamical dark energy (DE) cosmological model, with ΛCDM parameters fixed by other observations, we further show that in our best(worst)- case scenario ∼5.9 per cent (∼12.3 per cent) relative uncertainties at the 90 per cent credible level can be obtained on w0, the DE equation of state parameter. Besides being relevant in their own right, EMRI measurements will be affected by different systematics compared to both EM and ground-based GW observations. Cross-validation with complementary cosmological measurements will therefore be of paramount importance, especially if convincing evidence of physics beyond ΛCDM emerges from future observations.