Decaying cold dark matter and the evolution of the cluster abundance

The cluster abundance and its redshift evolution are known to be powerful tools for constraining the amplitude of mass fluctuations sigma(8) and the mass density parameter Omega(m0). We study the impact of the finite decay rate of cold dark matter particles on the cluster abundances. On the basis of a spherical model in a decaying cold dark matter universe, we calculate the mass function of clusters and compare it with observed cluster abundance. We find the decay of cold dark matter particles significantly changes the evolution of the cluster abundance. In particular, we point out that the lifetime of dark matter particles comparable to the age of the universe lowers the ratio of the local cluster abundance to the high-redshift cluster abundance and can account for the observed evolution of the cluster abundance quite well. The strong dependence of the cluster abundance on the decay rate of dark matter suggests that distant cluster surveys may offer clues to the nature of dark matter.