Soon after it was proposed, it was realized that SZE observations could yield distances to galaxy clusters when combined with X-ray data. SZE/X-ray distances are independent of the extragalactic distance ladder and do not rely on clusters being standard candles or rulers. The promise of direct distances helped motivate searches for the SZE in galaxy clusters. It is only in recent years that observations of the small ( 1 mK) SZE signal have yielded reliable detections and imaging, mostly due to advances in observational techniques.
SZE/X-ray distances have progressed from distance determinations one cluster at a time to samples of tens of galaxy clusters. To date, there are 41 SZE/X-ray determined distances to 26 different galaxy clusters. The combined 41 cluster distances imply a Hubble parameter of ~ 61 ± 3 ± 18 km s-1 Mpc-1, where the approximate uncertainties are statistical followed by systematic at 68% confidence. Shared systematics between the determined distances make it difficult to determine them precisely. For example, multiple distance determinations to a single galaxy cluster overstress any asphericity and orientation effects. There are three homogeneously analyzed samples of clusters consisting of five, seven, and 18 galaxy clusters. Even with these small samples, systematics clearly dominate. Systematic uncertainties are approachable with current X-ray and radio observatories.
SZE/X-ray determined direct distances to galaxy clusters are beginning to trace out the theoretical angular-diameter distance relation. It is clear that with a large sample of galaxy clusters at high redshift, SZE/X-ray distances will be able to determine the geometry of the Universe. In fact, if for some (highly unlikely) reason there was a systematic offset with the SZE/X-ray distances, the shape of the curve could still be determined and cosmological parameters inferred.
The redshift independence of the SZE will be exploited with surveys of large patches of sky with next generation, dedicated SZE experiments. Such surveys will provide large catalogs of clusters, many of which will be at high redshift (z > 1), providing large enough samples to use SZE/X-ray distances to determine both the Hubble constant and the geometry of the Universe. In addition, the cluster yields from deep, large-scale SZE surveys are critically dependent on the cosmology, potentially allowing a determination of the equation of state of the "dark energy." High-resolution SZE, X-ray, and optical (including weak lensing) observations will provide insights into the evolution and structure of the cluster gas necessary to exploit fully the evolution in cluster yields from SZE surveys.
The author is grateful for financial support from NASA Chandra Postdoctoral Fellowship PF 1-20020.