The three-point function as a probe of models for large-scale structure

Abstract

The authors analyze the consequences of models of structure formation for higher-order (n-point) galaxy correlation functions in the mildly non-linear regime. Several variations of the standard [Omega] = 1 cold dark matter model with scale-invariant primordial perturbations have recently been introduced to obtain more power on large scales, R[sub p] [approximately]20 h[sup [minus]1] Mpc, e.g., low-matter-density (non-zero cosmological constant) models, [open quote]tilted[close quote] primordial spectra, and scenarios with a mixture of cold and hot dark matter. They also include models with an effective scale-dependent bias, such as the cooperative galaxy formation scenario of Bower, et al. The authors show that higher-order (n-point) galaxy correlation functions can provide a useful test of such models and can discriminate between models with true large-scale power in the density field and those where the galaxy power arises from scale-dependent bias: a bias with rapid scale-dependence leads to a dramatic decrease of the hierarchical amplitudes Q[sub J] at large scales, r [approx gt] R[sub p]. Current observational constraints on the three-point amplitudes Q[sub 3] and S[sub 3] can place limits on the bias parameter(s) and appear to disfavor, but not yet rule out, the hypothesis that scale-dependent bias is responsible for the extra power observed on large scales.