http://arxiv.org/PS_cache/astro-ph/pdf/0508/0508526.pdf Title: The effects of Population III stars and variable IMF on the chemical evolution of the Galaxy Authors: Silvia Kuna Ballero, Francesca Matteucci, Cristina Chiappini Comments: 30 pages, 10 figures, accepted for publication in New Astronomy We studied the effects of a hypothetical initial stellar generation (PopIII) of only massive and very massive stars (VMS) on the chemical evolution of the Galaxy. We adopted the two-infall chemical evolution model of Chiappini et al. and tested several sets of yields for primordial VMS (Pair-Creation SNe), which produce different amounts of heavy elements than lower mass stars. We focused on the evolution of alpha-elements, C, N, Fe. The effects of PopIII stars on the Galactic evolution of these elements is negligible if a few generations of such stars occurred, whereas they produce different results from the standard models if they formed for a longer period. Also the effects of a more strongly variable IMF were discussed, making use of suggestions appeared in the literature to explain the lack of metal-poor stars in the Galactic halo with respect to model predictions. The predicted variations in abundances, SN rates, G-dwarf [Fe/H] distribution are here more dramatic and in contrast with observations; we concluded that a constant or slightly varying IMF is the best solution. Our main conclusion is that if VMS existed they must have formed only for a very short period of time (until the halo gas reached the threshold metallicity for the formation of very massive objects); in this case, their effects on the evolution of the studied elements was negligible also in the earliest phases. We thus cannot prove or disprove the existence of such stars on the basis of the available data. Due to their large metal production and short lives, primordial VMS should have enriched the halo gas beyond the metallicity of the most metal poor stars known in a few Myrs. This constrains the number of Pair-Creation SNe: we find that a number of 2-20 of such SNe occurred in our Galaxy depending on the stellar yields.