Energy injection and absorption in the cosmic dark ages

Dark matter annihilation or deexcitation, decay of metastable species, or other new physics may inject energetic electrons and photons into the photon-baryon fluid during and after recombination. As such particles cool, they partition their energy into a large number of efficiently ionizing electrons and photons, which in turn modify the ionization history. Recent work has provided a simple method for constraining arbitrary energy-deposition histories using the cosmic microwave background (CMB); in this note, we present results describing the energy-deposition histories for photons and electrons as a function of initial energy and injection redshift. With these results, the CMB bounds on any process injecting some arbitrary spectrum of electrons, positrons and/or photons with arbitrary redshift dependence can be immediately computed.