Measuring cosmic distances with galaxy clusters
  In addition to cosmological tests based on the mass function and clustering
of galaxy clusters, which probe the growth of cosmic structure, nature offers
two independent ways of using clusters to measure cosmic distances. The first
uses measurements of the X-ray emitting gas mass fraction, which is an
approximately standard quantity, independent of mass and redshift, for the most
massive clusters. The second uses combined millimeter (mm) and X-ray
measurements of cluster pressure profiles. We review these methods, their
current status and the prospects for improvements over the next decade. For the
first technique, which currently provides comparable dark energy constraints to
type Ia supernova studies, improvements of a factor of 6 or more should be
readily achievable, together with tight constraints on the mean matter density
that are largely independent of the cosmological model assumed. Realizing this
potential will require a coordinated, multiwavelength approach, utilizing new
cluster surveys, X-ray, optical and mm facilities, and a continued emphasis on
improved hydrodynamical simulations.
