  [Abridged] Understanding how the intergalactic medium (IGM) was reionized at
z > 6 is one of the big challenges of current high redshift astronomy. It
requires modelling the collapse of the first astrophysical objects (Pop III
stars, first galaxies) and their interaction with the IGM, while at the same
time pushing current observational facilities to their limits. The
observational and theoretical progress of the last few years have led to the
emergence of a coherent picture in which the budget of hydrogen-ionizing
photons is dominated by low-mass star-forming galaxies, with little
contribution from Pop III stars and quasars. The reionization history of the
Universe therefore critically depends on the number density of low-mass
galaxies at high redshift. In this work, we explore how changes in the
statistical properties of initial density fluctuations affect the formation of
early galaxies. Following Habouzit et al. (2014), we run 5 N-body simulations
with Gaussian and (scale-dependent) non-Gaussian initial conditions, all
consistent with Planck constraints. By appealing to a galaxy formation model
and to a population synthesis code, we compute the far-UV galaxy luminosity
function down to M_UV = -14 at redshift 7 < z < 15. We find that models with
strong primordial non-Gaussianities on < Mpc scales show a far-UV luminosity
function significantly enhanced in low-mass galaxies. We adopt a reionization
model calibrated from state-of-the-art hydrodynamical simulations and show that
such non-Gaussianities leave a clear imprint on the Universe reionization
history and electron Thomson scattering optical depth tau_E. Although current
uncertainties in the physics of reionization and on the determination of tau_E
still dominate the signatures of non-Gaussianities, our results suggest that
tau_E could ultimately be used to constrain the statistical properties of
initial density fluctuations.
