Cosmology with the Sunyaev-Zel'dovich effect

The Sunyaev-Zel'dovich effect (SZE) provides a unique way to map the large-scale structure of the universe as traced by massive clusters of galaxies. As a spectral distortion of the cosmic microwave background, the SZE is insensitive to the redshift of the galaxy cluster, making it well-suited for studies of clusters at all redshifts, and especially at reasonably high redshifts (z > 1) where the abundance of clusters is critically dependent on the underlying cosmology. Recent high signal-to-noise detections of the SZE have enabled interesting constraints on the Hubble constant and on the matter density of the universe using small samples of galaxy clusters. Upcoming SZE surveys are expected to find hundreds to thousands of new galaxy clusters, with a mass selection function that is remarkably uniform with redshift. In this review we provide an overview of the SZE and its use for cosmological studies, with emphasis on the cosmology that can, in principle, be extracted from SZE survey yields. We discuss the observational and theoretical challenges that must be met before precise cosmological constraints can be extracted from the survey yields.