Searching for Dark Matter in the CMB: A Compact Parameterization of
  Energy Injection from New Physics
  High-precision measurements of the temperature and polarization anisotropies
of the cosmic microwave background radiation have been previously employed to
set robust constraints on dark matter annihilation during recombination. In
this work we improve and generalize these constraints to apply to energy
deposition during the recombination era with arbitrary redshift dependence. Our
approach also provides more rigorous and model-independent bounds on dark
matter annihilation and decay scenarios. We employ principal component analysis
to identify a basis of weighting functions for the energy deposition. The
coefficients of these weighting functions parameterize any energy deposition
model and can be constrained directly by experiment. For generic energy
deposition histories that are currently allowed by WMAP7 data, up to 3
principal component coefficients are measurable by Planck and up to 5
coefficients are measurable by an ideal cosmic variance limited experiment. For
WIMP dark matter, our analysis demonstrates that the effect on the CMB is
described well by a single (normalization) parameter and a "universal" redshift
dependence for the energy deposition history. We give WMAP 7 constraints on
both generic energy deposition histories and the universal WIMP case.
