We calculate the contribution to the cosmic infrared background from very massive metal-free stars at high redshift. We explore two plausible star-formation models and two limiting cases for the reprocessing of the ionizing stellar emission. We find that Population III stars may contribute significantly to the cosmic near-infrared background if the following conditions are met: (i) The first stars were massive, with M > ~100 M_sun. (ii) Molecular hydrogen can cool baryons in low-mass haloes. (iii) Pop III star formation is ongoing, and not shut off through negative feedback effects. (iv) Virialized haloes form stars at about 40 per cent efficiency up to the redshift of reionization, z~7. (v) The escape fraction of the ionizing radiation into the intergalactic medium is small. (vi) Nearly all of the stars end up in massive black holes without contributing to the metal enrichment of the Universe.
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