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Gravitational-wave cosmology began in 2017 with the observation of thegravitational waves emitted in the merger of two neutron stars, and thecoincident observation of the electromagnetic emission that followed. Althoughonly a $30\%$ measurement of the Hubble constant was achieved, futureobservations may yield more precise measurements either through othercoincident events or through cross correlation of gravitational-wave eventswith galaxy catalogs. Here, we implement a new way to measure the Hubbleconstant without an electromagnetic counterpart and through the use of thebinary Love relations. These relations govern the tidal deformabilities ofneutron stars in an equation-of-state insensitive way. Importantly, the Loverelations depend on the component masses of the binary in the source frame.Since the gravitational-wave phase and amplitude depend on the chirp mass inthe observer (and hence redshifted) frame, one can in principle combine thebinary Love relations with the gravitational-wave data to directly measure theredshift, and thereby infer the value of the Hubble constant. We implement thisapproach in both real and synthetic data through a Bayesian parameterestimation study in a range of observing scenarios. We find that for theLIGO/Virgo/KAGRA design sensitivity era, this method results in a similarmeasurement accuracy of the Hubble constant to those of current-day, dark-sirenmeasurements. For third generation detectors, this accuracy improves to$\lesssim 10\%$ when combining measurements from binary neutron star events inthe LIGO Voyager era, and to $\lesssim 2\%$ in the Cosmic Explorer era.

Cosmology with Love: Measuring the Hubble constant using neutron star universal relations