Department of Physics, The University of Tokyo,
Tokyo 113-0033, Japan
2. Research Center for the Early University, School of Science, The University of Tokyo, Tokyo 113-0033, Japan
3. Astronomical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
4. Nobeyama Radio Observatory, Minamimaki, Minamisaku, Nagano 384-1305, Japan
5. Astrophysics Research Institute, Liverpool John Moores University, Byrom Street, Liverpool L3 3AF, UK
6. Department of Astronomy, Kyoto University, Kyoto 606-8502, Japan
Cosmological implications of clusters of galaxies are discussed with particular attention to their importance in probing the cosmological parameters. More specifically we compute the number counts of clusters of galaxies, Log $N$ -- Log $S$ relation, in X-ray and submm bands on the basis of the Press--Schechter theory. As an important step toward breaking the degeneracy among the viable cosmological models, we observed the most luminous X-ray cluster RXJ1347-1145 in three bands (21 and 43 GHz in the Nobeyama Radio Observatory, Japan, and 350 GHz in the J. C. Maxwell telescope at Mauna Kea, Hawaii). We report on the preliminary results which are in good agreement with the profile of the Sunayev -- Zel'dovich effect predicted on the basis of the previous X-ray observation of the cluster.