On the Origin and Evolution of the Galaxy Stellar Mass Function
  Here we explore the evolution of galaxy ensembles at early times by writing
the in situ stellar mass growth of galaxies purely as a stationary stochastic
(e.g., quasi-steady state) process. By combining the mathematics of such
processes with Newtonian gravity and a mean local star formation efficiency, we
show that the stellar mass evolution of galaxy ensembles is directly related to
the average acceleration of baryons onto dark matter halos at the onset of star
formation, with explicit dependencies on initial local matter densities and
halo mass. The density term specifically implies more rapid average rates of
growth in higher density regions of the universe compared to low density
regions, i.e., assembly bias. With this framework, using standard cosmological
parameters, a mean star formation efficiency derived by other authors, and
knowledge of the shape of the cosmological matter power spectrum at small
scales, we analytically derive (1) the characteristic stellar masses of
galaxies (M*), (2) the power-law low-mass slope (alpha) and normalization
(phi*) of the stellar mass function, and (3) the evolution of the stellar mass
function in time over 12.5 > z > 2. Correspondingly, the rise in the cosmic
star formation rate density over these epochs, while the universe can sustain
unabated fueling of star formation, also emerges naturally. All of our findings
are consistent with the deepest available data, including the expectation of
alpha~-7/5; i.e., a stellar mass function low-mass slope that is notably
shallower than that of the halo mass function, and with no systematic
deviations from a mean star formation efficiency with density or mass, nor any
explicit, additional feedback mechanisms. These derivations yield a compelling
richness and complexity but also show that very few astrophysical details are
required to understand the evolution of cosmic ensemble of galaxies at early
times.
