Phase Correlations and Topological Measures of Large-Scale Structure

The process of gravitational instability initiated by small primordial density perturbations is a vital ingredient of cosmological models that attempt to explain how galaxies and large-scale structure formed in the Universe. In the standard picture (the “concordance” model), a period of accelerated expansion (“inflation”) generated density fluctuations with simple statistical properties through quantum processes (Starobinsky [82], [83], [84]; Guth [39]; Guth & Pi [40]; Albrecht & Steinhardt [2]; Linde [55]). In this scenario the primordial density field is assumed to form a statistically homogeneous and isotropic Gaussian random field (GRF). Over years of observational scrutiny this paradigm has strengthened its hold in the minds of cosmologists and has survived many tests, culminating in those furnished by the Wilkinson Microwave Anisotropy Probe (WMAP; Bennett et al. [7]; Hinshaw et al. [45]