The cosmological constant and the clusters of galaxies

The dependence of the formation redshift of clusters of galaxies on the cosmological constant is discussed on the basis of recent measurements of gravitational masses and radii from X-ray astronomy techniques. For a flat CDM model with several different values of the cosmological constant, the cluster number density as a function of the redshift is calculated. Comparing the calculated number density at z ? 0 with the observed value limits the spectrum parameter Γ to the range 0.15–0.32. We also show that if Γ and/or Ω_Λ were larger, many more clusters of galaxies would have been formed at high redshifts.