Self-consistency and calibration of cluster number count surveys for dark energy

Cluster number counts offer sensitive probes of the dark energy if and only if the evolution of the cluster mass versus observable relation(s) is well calibrated. We investigate the potential for internal calibration by demanding consistency in the counts as a function of the observable. In the context of a constant dark energy equation of state, the known initial fluctuation amplitude expected from the cosmic microwave background, universal underlying mass function, and an idealized selection, we find that the ambiguity from the normalization of the mass-observable relationships, or an extrapolation of external mass-observable determinations from higher masses, can be largely eliminated with a sufficiently deep survey, even allowing for an arbitrary evolution. More generally, number counts as a function of both the redshift and the observable enable strong consistency tests on assumptions made in modeling the mass-observable relations and cosmology.