  Observation of even a single massive cluster, especially at high redshift,
can falsify the standard cosmological framework consisting of a cosmological
constant and cold dark matter (LCDM) with Gaussian initial conditions by
exposing an inconsistency between the well-measured expansion history and the
growth of structure it predicts. Through a likelihood analysis of current
cosmological data that constrain the expansion history, we show that the LCDM
upper limits on the expected number of massive, distant clusters are nearly
identical to limits predicted by all quintessence models where dark energy is a
minimally coupled scalar field with a canonical kinetic term. We provide
convenient fitting formulas for the confidence level at which the observation
of a cluster of mass M at redshift z can falsify LCDM and quintessence given
cosmological parameter uncertainties and sample variance, as well as for the
expected number of such clusters in the light cone and the Eddington bias
factor that must be applied to observed masses. By our conservative confidence
criteria, which equivalently require masses 3 times larger than typically
expected in surveys of a few hundred square degrees, none of the presently
known clusters falsify these models. Various systematic errors, including
uncertainties in the form of the mass function and differences between
supernova light curve fitters, typically shift the exclusion curves by less
than 10% in mass, making current statistical and systematic uncertainties in
cluster mass determination the most critical factor in assessing falsification
of LCDM and quintessence.
