Abstract
An exact relativistic single-integral formula for the thermal average of the annihilation cross section times velocity, the key quantity in the determination of the cosmic relic abundance of a species, is obtained. Since it does not require expansion of the cross section at low relative velocity, it can also be used when the cross section varies rapidly with energy, e.g. near the formation of a resonance or the opening of a new annihilation channel. We discuss approximate formulas in these cases, and we find that dips in the relic density near resonances are significantly broader and shallower than previously thought and that spurious reductions near thresholds disappear.
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