Tracing the nature of dark energy with galaxy distribution

Dynamical dark energy (DE) is a viable alternative to the cosmological constant. Constructing tests to discriminate between Lambda and dynamical DE models is difficult, however, because the differences are not large. In this paper we explore tests based on the galaxy mass function, the void probability function (VPF), and the number of galaxy clusters. At high z, the number density of clusters shows large differences between DE models, but geometrical factors reduce the differences substantially. We find that detecting a model dependence in the cluster redshift distribution is a significant challenge. We show that the galaxy redshift distribution is potentially a more sensitive characteristic. We do this by populating dark matter haloes in N-body simulations with galaxies using well-tested halo occupation distributions. We also estimate the VPF and find that samples with the same angular surface density of galaxies, in different models, exhibition almost model-independent VPF which therefore cannot be used as a test for DE. Once again, geometry and cosmic evolution compensate each other. By comparing VPFs for samples with fixed galaxy mass limits, we find measurable differences.