We contrast predictions for the high-redshift galaxy population and reionization history between cold dark matter (CDM) and an alternative self-interacting dark matter model based on the recently developed ETHOS framework that alleviates the small-scale CDM challenges within the Local Group. We perform the highest resolution hydrodynamical cosmological simulations (a 36~Mpc$^3$ volume with gas cell mass of $sim10^5mathrm{M}_{odot}$ and minimum gas softening of $sim180$~pc) within ETHOS to date -- plus a CDM counterpart -- to quantify the abundance of galaxies at high redshift and their impact on reionization. We find that ETHOS predicts galaxies with higher ultraviolet (UV) luminosities than their CDM counterparts and a faster build-up of the faint end of the UV luminosity function. These effects, however, make the optical depth to reionization less sensitive to the power spectrum cut-off: the ETHOS model differs from the CDM $tau$ value by only 10 per cent and is consistent with Planck limits if the effective escape fraction of UV photons is 0.1-0.5. We conclude that current observations of high-redshift luminosity functions cannot differentiate between ETHOS and CDM models, but deep JWST surveys of strongly-lensed, inherently faint galaxies have the potential to test non-CDM models that offer attractive solutions to CDMs Local Group problems.
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