The mass evolution of the first galaxies: stellar mass functions and
  star formation rates at $4 < z < 7$ in the CANDELS GOODS-South field
  We measure new estimates for the galaxy stellar mass function and star
formation rates for samples of galaxies at $z \sim 4,~5,~6~\&~7$ using data in
the CANDELS GOODS South field. The deep near-infrared observations allow us to
construct the stellar mass function at $z \geq 6$ directly for the first time.
We estimate stellar masses for our sample by fitting the observed spectral
energy distributions with synthetic stellar populations, including nebular line
and continuum emission. The observed UV luminosity functions for the samples
are consistent with previous observations, however we find that the observed
$M_{UV}$ - M$_{*}$ relation has a shallow slope more consistent with a constant
mass to light ratio and a normalisation which evolves with redshift. Our
stellar mass functions have steep low-mass slopes ($\alpha \approx -1.9$),
steeper than previously observed at these redshifts and closer to that of the
UV luminosity function. Integrating our new mass functions, we find the
observed stellar mass density evolves from $\log_{10} \rho_{*} =
6.64^{+0.58}_{-0.89}$ at $z \sim 7$ to $7.36\pm0.06$ $\text{M}_{\odot}
\text{Mpc}^{-3}$ at $z \sim 4$. Finally, combining the measured UV continuum
slopes ($\beta$) with their rest-frame UV luminosities, we calculate dust
corrected star-formation rates (SFR) for our sample. We find the specific
star-formation rate for a fixed stellar mass increases with redshift whilst the
global SFR density falls rapidly over this period. Our new SFR density
estimates are higher than previously observed at this redshift.
