CMB bounds on dark matter annihilation: Nucleon energy losses after recombination

We consider the propagation and energy losses of protons and antiprotons produced by dark matter annihilation at redshifts 100<z≲2000. In the case of dark matter annihilations into quarks, gluons and weak gauge bosons, protons and antiprotons carry about 20% of the energy injected into e± and γ’s, but their interactions are normally neglected when deriving cosmic microwave background bounds from altered recombination histories. Here, we follow numerically the energy-loss history of typical protons/antiprotons in the cosmological medium. We show that about half of their energy is channeled into photons and e±, and we present a simple prescription to estimate the corresponding strengthening of the cosmic microwave background bounds on the dark matter annihilation cross section.