Mapping Galaxy Clusters in the Distant Universe

We present the science case for mapping several thousand galaxy (proto)clusters at z=1-10 with a large aperture single dish sub-mm facility, producing a high-redshift counterpart to local large surveys of rich clusters like the well-studied Abell catalogue. Principal goals of a large survey of distant clusters are the evolution of galaxy clusters over cosmic time and the impact of environment on the evolution and formation of galaxies. To make a big leap forward in this emerging research field, the community would benefit from a large-format, wide-band, direct-detection spectrometer (e.g., based on MKID technology), covering a wide field of ~1 square degree and a frequency coverage from 70 to 700 GHz.