  Near-infrared surveys have now determined the luminosity functions of
galaxies at 6<z<9 to impressive precision and identified a number of candidates
at even earlier times. Here we develop a simple analytic model to describe
these populations that allows physically-motivated extrapolation to earlier
times and fainter luminosities. We assume that galaxies grow through accretion
onto dark matter halos, which we model by matching halos at fixed number
density across redshift, and that stellar feedback limits the star formation
rate. We allow for a variety of feedback mechanisms, including regulation
through supernova energy and momentum from radiation pressure. We show that
reasonable choices for the feedback parameters can fit the available galaxy
data, which in turn substantially limits the range of plausible extrapolations
of the luminosity function to earlier times and fainter luminosities: for
example, the global star formation rate declines rapidly at z>10, but the
bright galaxies accessible to observations decline much faster than the total.
Deviations from our predictions would provide evidence for new astrophysics
within the first generations of galaxies. We also provide predictions for
galaxy measurements by future facilities, including JWST and WFIRST.

Astrophysics of Galaxies