Gravity and the non-linear growth of structure in the Carnegie-Spitzer-IMACS Redshift Survey

 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 δ – the density relative to the median – should grow as $\delta (t)\propto \delta _{0}^{\alpha }\, t^{\beta }$, where α ≡ 2 and β ≡ 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 (∼7 Gyr) and infer α = 1.98 ± 0.04 and β = 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.