The remarkable HST datasets from the CANDELS , HUDF09 , HUDF12 , ERS , and BoRG/HIPPIES programs have allowed us to map the evolution of the rest-frame UV luminosity function from z \sim 10 to z \sim 4 .
We develop new color criteria that more optimally utilize the full wavelength coverage from the optical , near-IR , and mid-IR observations over our search fields , while simultaneously minimizing the incompleteness and eliminating redshift gaps .
We have identified 5859 , 3001 , 857 , 481 , 217 , and 6 galaxy candidates at z \sim 4 , z \sim 5 , z \sim 6 , z \sim 7 , z \sim 8 , and z \sim 10 , respectively from the \sim 1000 arcmin ^ { 2 } area covered by these datasets .
This sample of > 10000 galaxy candidates at z \geq 4 is by far the largest assembled to date with HST .
The selection of z \sim 4 -8 candidates over the five CANDELS fields allows us to assess the cosmic variance ; the largest variations are at z \geq 7 .
Our new LF determinations at z \sim 4 and z \sim 5 span a 6-mag baseline and reach to - 16 AB mag .
These determinations agree well with previous estimates , but the larger samples and volumes probed here result in a more reliable sampling of > L ^ { * } galaxies and allow us to re-assess the form of the UV LFs .
Our new LF results strengthen our earlier findings to 3.4 \sigma significance for a steeper faint-end slope of the UV LF at z > 4 , with \alpha evolving from \alpha = -1.64 \pm 0.04 at z \sim 4 to \alpha = -2.06 \pm 0.13 at z \sim 7 ( and \alpha = -2.02 \pm 0.23 at z \sim 8 ) , consistent with that expected from the evolution of the halo mass function .
We find less evolution in the characteristic magnitude M ^ { * } from z \sim 7 to z \sim 4 ; the observed evolution in the LF is now largely represented by changes in \phi ^ { * } .
No evidence for a non-Schechter-like form to the z \sim 4 -8 LFs is found .
A simple conditional luminosity function model based on halo growth and evolution in the M/L ratio ( \propto ( 1 + z ) ^ { -1.5 } ) of halos provides a good representation of the observed evolution .