Testing time evolution of the mass distribution of the black hole
  mergers
  Detection of the gravitational-wave events revealed that there are numerous
population of the black hole binaries which can merge within the age of the
Universe. Although several formation channels of such binaries are known,
considerable theoretical uncertainties associated in each channel defeats the
robust prediction of how much each channel contributes to the total merger rate
density. Given that the time evolution of the merger rate density in some
channels is (exactly or nearly) independent of the BH masses, clarifying this
feature from the observational data will shed some light on the nature of the
black hole binaries. Based on this motivation, we formulate the methodology to
perform the statistical test of whether the mass distribution of the black hole
mergers evolves in time or not by means of the hypothesis testing. Our
statistical test requires neither a priori specification of the mass
distribution which is largely uncertain nor that of the time dependence of the
merger rate. We then apply it to the mock data for some concrete shapes of the
merger rate density and show that the proposed method rejects/(does not reject)
the null hypothesis correctly for the large sample size. We also investigate if
the catalog of the gravitational-wave events obtained during the LIGO-Virgo's
third observing run has a large sample size enough to apply our hypothesis
testing. We find that the number of the events is too small to draw any
statistical conclusion regarding our test and the meaningful result of our
hypothesis testing can be obtained only by the future detectors having much
better sensitivity. These results demonstrate the effectiveness of our
hypothesis testing to determine from the (future) observational data whether
the merger rate density evolves in time independently of the BH masses or not.
