Cosmic constraints rule out s-wave annihilation of light dark matter

Light dark matter annihilating into electron-positron pairs emits a significant amount of internal bremsstrahlung that may contribute to the cosmic gamma-ray background. The amount of emitted gamma-rays depends on the dark matter clumping factor. Recent calculations indicate that this value should be of order $10^6-10^7$. That allows us to calculate the expected gamma-ray background contribution from dark matter annihilation. We find that the light dark matter model can be ruled out if a constant thermally-averaged cross section is assumed (s-wave annihilation). For more massive dark matter candidates like neutralinos, however, cosmic constraints are weaker.