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A key obstacle to developing a satisfying theory of galaxy evolution is thedifficulty in extending analytic descriptions of early structure formation intofull nonlinearity, the regime in which galaxy growth occurs. Extant techniques,though powerful, are based on approximate numerical methods whose MonteCarlo-like nature hinders intuition building. Here, we develop a new solutionto this problem and its empirical validation. We first derive closed-formanalytic expectations for the evolution of fixed percentiles in the real-spacecosmic density distribution, {\it averaged over representative volumesobservers can track cross-sectionally\}. Using the Lagrangian forms of thefluid equations, we show that percentiles in $\delta$---the density relative tothe median---should grow as $\delta(t)\propto\delta_{0}^{\alpha}\,t^{\beta}$,where $\alpha\equiv2$ and $\beta\equiv2$ for Newtonian gravity at epochs afterthe overdensities transitioned to nonlinear growth. We then use 9.5 sq. deg. ofCarnegie-Spitzer-IMACS Redshift Survey data to map {\it galaxy\} environmentaldensities over $0.2<z<1.5$ ($\sim$7 Gyr) and infer $\alpha=1.98\pm0.04$ and$\beta=2.01\pm0.11$---consistent with our analytic prediction. Thesefindings---enabled by swapping the Eulerian domain of most work on densitygrowth for a Lagrangian approach to real-space volumetric averages---providesome of the strongest evidence that a lognormal distribution of early densityfluctuations indeed decoupled from cosmic expansion to grow throughgravitational accretion. They also comprise the first exact, analyticdescription of the nonlinear growth of structure extensible to (arbitrarily)low redshift. We hope these results open the door to new modeling of, andinsight-building into, the galaxy growth and its diversity in cosmologicalcontexts.

Gravity and the Nonlinear Growth of Structure in the Carnegie-Spitzer-IMACS Redshift Survey