The Evolution of Galaxy Number Density at z < 8 and its Implications
  The evolution of the number density of galaxies in the universe, and thus
also the total number of galaxies, is a fundamental question with implications
for a host of astrophysical problems including galaxy evolution and cosmology.
However there has never been a detailed study of this important measurement,
nor a clear path to answer it. To address this we use observed galaxy stellar
mass functions up to $z\sim8$ to determine how the number densities of galaxies
changes as a function of time and mass limit. We show that the increase in the
total number density of galaxies ($\phi_{\rm T}$), more massive than M$_{*} =
10^{6}$ M_0, decreases as $\phi_{\rm T} \sim t^{-1}$, where $t$ is the age of
the universe. We further show that this evolution turns-over and rather
increases with time at higher mass lower limits of M$_{*}>10^{7}$ M_0. By using
the M$_{*}=10^{6}$ M_0 lower limit we further show that the total number of
galaxies in the universe up to $z = 8$ is $2.0^{+0.7}_{-0.6} \times 10^{12}$
(two trillion), almost a factor of ten higher than would be seen in an all sky
survey at Hubble Ultra-Deep Field depth. We discuss the implications for these
results for galaxy evolution, as well as compare our results with the latest
models of galaxy formation. These results also reveal that the cosmic
background light in the optical and near-infrared likely arise from these
unobserved faint galaxies. We also show how these results solve the question of
why the sky at night is dark, otherwise known as Olbers' paradox.
