Dark stars powered by dark matter annihilation have been proposed as the first luminous sources in the universe. These stars are believed to form in the central dark matter cusp of low-mass minihalos. Recent calculations indicate stellar masses up to sim1000 solar masses and/or have very long lifetimes. The UV photons from these objects could therefore contribute significantly to cosmic reionization. Here we show that such dark star models would require a somewhat artificial reionization history, based on a double-reionization phase and a late star-burst near redshift $zsim6$, in order to fulfill the WMAP constraint on the optical depth as well as the Gunn-Peterson constraint at $zsim6$. This suggests that, if dark stars were common in the early universe, then models are preferred which predict a number of UV photons similar to conventional Pop. III stars. This excludes dark stars with 100 solar masses that enter a main-sequence phase and other models that lead to a strong increase in the number of UV photons. We also derive constraints for massive as well as light dark matter candidates from the observed X-ray, gamma-ray and neutrino background, considering dark matter profiles which have been steepened during the formation of dark stars. This increases the clumping factor at high redshift and gives rise to a higher dark matter annihilation rate in the early universe. We furthermore estimate the potential contribution from the annihilation products in the remnants of dark stars, which may provide a promising path to constrain such models further, but which is currently still uncertain.
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