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. There is, however, a perfect degeneracy between the source masses and redshift; some nongravitational 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 ∼ 45 M , 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 a realistic BBH merger rate, mass distribution with smooth PISN cutoff, and measurement uncertainty. We show that after one year of operation at design sensitivity the BBH population can constrain H(z) to 6.1% at a pivot redshift z 0.8. After five years the constraint improves to 2.9%. If the PISN cutoff is sharp, the uncertainty is smaller by about a factor of two. This measurement relies only on general relativity and the presence of a mass scale that is approximately fixed or calibrated across cosmic time; it is independent of any distance ladder. Observations by future "third-generation" gravitational wave (GW) detectors, which can

We study the evolution of the binary black hole (BBH) mass distribution across cosmic time. The second gravitational-wave transient catalog (GWTC-2) from LIGO/Virgo contains BBH events out to redshifts z ∼ 1, with component masses in the range ∼5–80 M ⊙. In this catalog, the biggest BBHs, with m 1 ≳ 45 M ⊙, are only found at the highest redshifts, z ≳ 0.4. We ask whether the absence of high-mass observations at low redshift indicates that the mass distribution evolves: the biggest BBHs only merge at high redshift, and cease merging at low redshift. Modeling the BBH primary-mass spectrum as a power law with a sharp maximum mass cutoff (Truncated model), we find that the cutoff increases with redshift (> 99.9% credibility). An abrupt cutoff in the mass spectrum is expected from (pulsational) pair-instability supernova simulations; however, GWTC-2 is only consistent with a Truncated mass model if the location of the cutoff increases from at z < 0.4 to at z > 0.4. Alternatively, if the primary-mass spectrum has a break in the power law (Broken Power Law) at , rather than a sharp cutoff, the data are consistent with a nonevolving mass distribution. In this case, the overall rate of mergers, at all masses, increases with redshift. Future observations will distinguish between a sharp mass cutoff that evolves with redshift and a nonevolving mass distribution with a gradual taper, such as a Broken Power Law. After ∼100 BBH merger observations, a continued absence of high-mass, low-redshift events would provide a clear signature that the mass distribution evolves with redshift.