  We compare model results from a semi-analytic (merger-tree based) framework
for high-redshift (z ~ 5-20) galaxy formation against reionization indicators,
including the Planck electron scattering optical depth and the ionizing photon
emissivity, to shed light on the reionization history and sources in Cold (CDM)
and Warm Dark Matter (WDM; particle masses of $m_x = 1.5,3$ and 5 keV)
cosmologies. This model includes all the key processes of star formation,
supernova feedback, the merger/accretion/ejection driven evolution of gas and
stellar mass and the effect of the ultra-violet background (UVB) in
photo-evaporating the gas content of low-mass galaxies. We find that the delay
in the start of reionization in light (1.5 keV) WDM models can be compensated
by a steeper redshift evolution of the ionizing photon escape fraction and a
faster mass assembly, resulting in reionization ending at comparable redshifts
(z~5.5) in all the DM models considered. We find the bulk of the reionization
photons come from galaxies with a halo mass $M_h < 10^9 M_\odot$ and a UV
magnitude $ -15 < M_{UV} < -10$ in CDM. The progressive suppression of low-mass
halos with decreasing $m_x$ leads to a shift in the reionization population to
larger halo masses of $M_h > 10^9 M_\odot$ and $ -17 < M_{UV} < -13$ for 1.5
keV WDM. We find that current observations of the electron scattering optical
depth and the Ultra-violet luminosity function are equally compatible with all
the (cold and warm) DM models considered in this work. We propose that global
indicators including the redshift evolution of the stellar mass density and the
stellar mass-halo mass relation, observable with the James Webb Space
Telescope, can be used to distinguish between CDM and WDM (1.5 keV)
cosmologies.
