Motivated by the WMAP results indicating an early epoch of reionization, we consider alternative cosmic star formation models which are capable of reionizing the early intergalactic medium. We develop models which include an early burst of massive stars (with several possible mass ranges) combined with standard star formation, in the framework of the hierarchical scenario of structure formation. We compute as a function of redshift the stellar ionizing flux of photons, the supernova rates and the chemical evolution, both in the intergalactic medium and in the interstellar medium of forming galaxies. We apply constraints from the cosmic observed star formation rate and the observed abundances in the Lyman $\alpha$ forest and in Damped Lyman $\alpha$ clouds in conjunction with the ability of the models to produce the required degree of reionization.