A Gravitational Ising Model for the Statistical Bias of Galaxies

Evaluation of gravitational theories by means of cosmological data suffers from the fact that galaxies are biased tracers of dark matter. Current bias models focus primarily on high-density regions, whereas low-density regions carry significant amounts of information relevant to the constraint of dark energy and alternative gravity theories. Thus, proper treatment of both high and low densities is important for future surveys. Accordingly, we here present an interactionless Ising model for this bias, and we demonstrate that it exhibits a remarkably good fit to both Millennium Simulation and Sloan Digital Sky Survey data, at both density extremes. The quality of the fit indicates that galaxy formation is (to first order) an essentially local process determined by initial conditions.