The Local Group as a time machine: studying the high-redshift Universe
  with nearby galaxies
  We infer the UV luminosities of Local Group galaxies at early cosmic times
($z \sim 2$ and $z \sim 7$) by combining stellar population synthesis modeling
with star formation histories derived from deep color-magnitude diagrams
constructed from Hubble Space Telescope (HST) observations. Our analysis
provides a basis for understanding high-$z$ galaxies - including those that may
be unobservable even with the James Webb Space Telescope (JWST) - in the
context of familiar, well-studied objects in the very low-$z$ Universe. We find
that, at the epoch of reionization, all Local Group dwarfs were less luminous
than the faintest galaxies detectable in deep HST observations of blank fields.
We predict that JWST will observe $z \sim 7$ progenitors of galaxies similar to
the Large Magellanic Cloud today; however, the HST Frontier Fields initiative
may already be observing such galaxies, highlighting the power of gravitational
lensing. Consensus reionization models require an extrapolation of the observed
blank-field luminosity function at $z \approx 7$ by at least two orders of
magnitude in order to maintain reionization. This scenario requires the
progenitors of the Fornax and Sagittarius dwarf spheroidal galaxies to be
contributors to the ionizing background at $z \sim 7$. Combined with numerical
simulations, our results argue for a break in the UV luminosity function from a
faint-end slope of $\alpha \sim -2$ at $M_{\rm UV} < -13$ to $\alpha \sim -1.2$
at lower luminosities. Applied to photometric samples at lower redshifts, our
analysis suggests that HST observations in lensing fields at $z \sim 2$ are
capable of probing galaxies with luminosities comparable to the expected
progenitor of Fornax.
