Indirect Dark Matter Signatures in the Cosmic Dark Ages I. Generalizing
  the Bound on s-wave Dark Matter Annihilation from Planck
  Recent measurements of the cosmic microwave background (CMB) anisotropies by
Planck provide a sensitive probe of dark matter annihilation during the cosmic
dark ages, and specifically constrain the annihilation parameter
$f_\mathrm{eff} \langle \sigma v \rangle/m_\chi$. Using new results (Paper II)
for the ionization produced by particles injected at arbitrary energies, we
calculate and provide $f_\mathrm{eff}$ values for photons and $e^+e^-$ pairs
injected at keV-TeV energies; the $f_\mathrm{eff}$ value for any dark matter
model can be obtained straightforwardly by weighting these results by the
spectrum of annihilation products. This result allows the sensitive and robust
constraints on dark matter annihilation presented by the Planck Collaboration
to be applied to arbitrary dark matter models with $s$-wave annihilation. We
demonstrate the validity of this approach using principal component analysis.
As an example, we integrate over the spectrum of annihilation products for a
range of Standard Model final states to determine the CMB bounds on these
models as a function of dark matter mass, and demonstrate that the new limits
generically exclude models proposed to explain the observed high-energy rise in
the cosmic ray positron fraction. We make our results publicly available at
http://nebel.rc.fas.harvard.edu/epsilon.
