A Future Percent-level Measurement of the Hubble Expansion at Redshift 0.8 with Advanced LIGO

Simultaneous measurements of distance and redshift can be used to constrain the expansion history of the universe and associated cosmological parameters. Merging binary black hole (BBH) systems are standard sirens---their gravitational waveform provides direct information about the luminosity distance to the source. Because gravity is scale-free, there is a perfect degeneracy between the source masses and redshift; some non-gravitational information is necessary to break the degeneracy and determine the redshift of the source. Here we suggest that the pair instability supernova (PISN) process, thought to be the source of the observed upper-limit on the black hole (BH) mass in merging BBH systems at $\sim 45 \, M_\odot$, imprints a mass scale in the population of BBH mergers and permits a measurement of the redshift-luminosity-distance relation with these sources. We simulate five years of BBH detections in the Advanced LIGO and Virgo detectors with realistic assumptions about the BBH merger rate, a mass distribution incorporating a smooth PISN cutoff, and measurement uncertainty. We show that after one year of operation at design sensitivity (circa 2021) the BBH population can constrain $H(z)$ to $6.1\%$ at a pivot redshift $z \simeq 0.8$. After five years (circa 2025) the constraint improves to $2.9\%$. This measurement relies only on general relativity and the presence of a cutoff mass scale that is approximately fixed or calibrated across cosmic time; it is independent of any distance ladder or cosmological model. Observations by future ``third-generation'' gravitational wave detectors, which can see BBH mergers throughout the universe, would permit sub-percent cosmographical measurements to $z \gtrsim 4$ within one month of observation.