Cosmic microwave background constraint on residual annihilations of relic particles

Energy injected into the cosmic microwave background at redshifts z10⁶ will distort its spectrum permanently. In this paper we discuss the distortion caused by annihilations of relic particles. We use the observational bounds on deviations from a Planck spectrum to constrain a combination of annihilation cross section, mass, and abundance. For particles with an (s-wave) annihilation cross section 〈σ|v|〉≡σ₀, the bound is ${f(m}X/MeV{)}^{{-}1}[({{σ}}₀/6×{}{10}^{{-}27} {cm}³{s}^{{-}1})({{Ω}}XX̄{h}²{)}²]<0.2,$ where ${m}X$ is the particle mass, ${{Ω}}XX̄$ is the fraction of the critical density the particle and its antiparticle contribute if they survive to the present time, ${h=H}₀/100 km{s}^{{-}1}{Mpc}^{{-}1},$ ${H}₀$ is the Hubble constant, and f is the fraction of the annihilation energy that interacts electromagnetically. We also compute the less stringent limits for p-wave annihilation. We update other bounds on residual annihilations and compare them to our CMB bound.