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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.