Abstract
A key obstacle to developing a satisfying theory of galaxy evolution is the difficulty in extending analytic descriptions of early structure formation into full non-linearity, the regime in which galaxy growth occurs. Extant techniques, though powerful, are based on approximate numerical methods whose Monte Carlo-like nature hinders intuition building. Here, we develop a new solution to this problem and its empirical validation. We first derive closed-form analytic expectations for the evolution of fixed percentiles in the real-space cosmic density distribution, averaged over representative volumes observers can track cross sectionally. Using the Lagrangian forms of the fluid equations, we show that percentiles in delta - the density relative to the median - should grow as delta(t) proportional to delta(alpha)(0) t(beta), where alpha 2 and beta 2 for Newtonian gravity at epochs after the overdensities transitioned to non-linear growth. We then use 9.5 square degress of Carnegie-Spitzer-IMACS Redshift Survey data to map galaxy environmental densities over 0.2 < z < 1.5 (similar to 7 Gyr) and infer alpha = 1.98 +/- 0.04 and beta = 2.01 +/- 0.11 - consistent with our analytic prediction. These findings - enabled by swapping the Eulerian domain of most work on density growth for a Lagrangian approach to real-space volumetric averages - provide some of the strongest evidence that a lognormal distribution of early density fluctuations indeed decoupled from cosmic expansion to grow through gravitational accretion. They also comprise the first exact, analytic description of the non-linear growth of structure extensible to (arbitrarily) low redshift. We hope these results open the door to new modelling of, and insight-building into, galaxy growth and its diversity in cosmological contexts.