Scaling Law of Exponents in Cosmological Clustering

The density of N-clusters (the cluster which contains N galaxies) in the universe is shown from observations to scale with N as n_N ∝ N^-τ with τ = 3/γ +1 and the correlation exponent γ ≈ 1.8. Correspondingly, a scaling relation τ = 29-9γ/12-4γ between the two exponents, which agrees with the observations, is found analytically in our naive clustering model.