We present a new technique to estimate the evolution of the very faint end of the UV luminosity function (LF) out to $zsim5$. 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 $zsim5$ 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.
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