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.
