The Very Faint End of the UV Luminosity Function over Cosmic Time:
  Constraints from the Local Group Fossil Record
  We present a new technique to estimate the evolution of the very faint end of
the UV luminosity function (LF) out to $z\sim5$. Measured star formation
histories (SFHs) from the fossil record of Local Group galaxies are used to
reconstruct the LF down to M$_{UV}\sim-5$ at $z\sim5$ and M$_{UV}\sim-1.5$ at
$z<1$. Such faint limits are well beyond the current observational limits and
are likely to remain beyond the limits of next generation facilities. The
reconstructed LFs, when combined with direct measurements of the LFs at higher
luminosity, are well-fit by a standard Schechter function with no evidence of a
break to the faintest limits probed by this technique. The derived faint end
slope, $\alpha$, steepens from $\approx-1.2$ at $z<1$ to $\approx-1.6$ at
$4<z<5$. We test the effects of burstiness in the SFHs and find the recovered
LFs to be only modestly affected. Incompleteness corrections for the faintest
Local Group galaxies and the (unlikely) possibility of significant
luminosity-dependent destruction of dwarf galaxies between high redshift and
the present epoch are important uncertainties. These and other uncertainties
can be mitigated with more detailed modeling and future observations. The
reconstructed faint end LF from the fossil record can therefore be a powerful
and complementary probe of the high redshift faint galaxies believed to play a
key role in the reionization of the Universe.
