  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 $z \sim 1$, with component
masses in the range $\sim5$--$80\,M_\odot$. In this catalog, the biggest black
holes, with $m_1 \gtrsim 45\,M_\odot$, are only found at the highest redshifts,
$z \gtrsim 0.4$. We ask whether the absence of high-mass BBH observations at
low redshift indicates that the astrophysical BBH mass distribution evolves:
the biggest BBHs only merge at high redshift, and cease merging at low
redshift. Alternatively, this feature might be explained by gravitational-wave
selection effects. 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 $45^{+13}_{-5}\,M_\odot$ at $z < 0.4$ to
$80^{+16}_{-13}\,M_\odot$ at $z > 0.4$. Alternatively, if the primary mass
spectrum has a break in the power law (Broken power law) at
${38^{+15}_{-8}\,M_\odot}$, rather than a sharp cutoff, the data are consistent
with a non-evolving mass distribution. In this case, the overall rate of
mergers, at all masses, increases with increasing redshift. Future observations
will confidently distinguish between a sharp maximum mass cutoff that evolves
with redshift and a non-evolving mass distribution with a gradual taper, such
as a Broken power law. After $\sim 100$ BBH merger observations, a continued
absence of high-mass, low-redshift events would provide a clear signature that
the mass distribution evolves with redshift.
