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We report our recent theoretical work on the evolution of grain size distribution and grain abundance, particularly focusing on high-redshift (high-z) galaxies. We consider dust production in supernovae and shattering in interstellar turbulence. We show that observed extinction curves at high z can be reproduced if the dust supplied from supernovae is processed by shattering in interstellar turbulence. We also calculate the evolution of grain abundance and compare our theoretical results with the observed dust abundances in high-redshift quasars. We find that shattering is crucial to activate grain mass increase by the accretion of gas-phase metals since small-grain production by shattering raises the grain growth rate significantly. This means that the evolution of grain size distribution plays a critical role in governing the dust abundance at high z.

We construct a semi-analytical model which includes a novel implementation of dust size evolution and the resulting H2 formation on dust grains in the early universe. We investigate the cosmic star formation rate and the reionization history, taking into acount the initial mass function transition from Pop III to Pop II stars due to dust cooling. We derive the star formation efficiencies for various host dark matter halo masses and discuss effects of the value of critical dust-to-gas mass ratio, Dcr, on the reionization history. We conclude that the reionization completes before z = 6 in the case of the fiducail value Dcr = 7.4×10−8.