Cosmological constraints on dark matter models with velocity-dependent annihilation cross section

We derive cosmological constraints on the annihilation cross section of dark matter with velocity-dependent structure, motivated by annihilating dark matter models through Sommerfeld or Breit-Wigner enhancement mechanisms. In models with an annihilation cross section increasing with decreasing dark matter velocity, a big-bang nucleosynthesis and cosmic microwave background give stringent constraints. Particularly, if the cross section is enhanced by a factor larger than 103, the thermal relic scenario is excluded for the dark matter lighter than O(TeV).