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Dark matter (DM) annihilation during hydrogen recombination (z1000) will alter the recombination history of the Universe, and affect the observed CMB temperature and polarization fluctuations. Unlike other astrophysical probes of DM, this is free of the significant uncertainties in modelling galactic physics, and provides a method to detect and constrain the cosmological abundances of these particles. We parametrize the effect of DM annihilation as an injection of ionizing energy at a rate ϵ₃₌, and argue that this simple ``on the spot'' modification is a good approximation to the complicated interaction of the annihilation products with the photon-electron plasma. Generic models of DM do not change the redshift of recombination, but change the residual ionization after recombination. This broadens the surface of last scattering, suppressing the temperature fluctuations and enhancing the polarization fluctuations. We use the temperature and polarization angular power spectra to measure these deviations from the standard recombination history, and therefore, indirectly probe DM annihilation. The modifications to the temperature power spectrum are nearly degenerate with the primordial scalar spectral index and amplitude; current CMB data are therefore unable to put any constraints on the annihilation power. This degeneracy is broken by polarization; Planck will have the sensitivity to measure annihilation power ϵ₃₌ (z=1000) >10^-15 eV/s/proton, while high sensitivity experiments (e. g. NASA's CMBpol) could improve that constraint to ϵ₃₌ (z=1000) >410^-16 eV/s/proton, assuming a fractional detector sensitivity of /T1 and a beam of 3^'. These limits translate into a lower bound on the mass of the DM particle, M₃₌>10-100 GeV, assuming a single species with a cross section of ⟨₀v⟩210^-26 cm^3/s, and a fraction f0. 1-1 of the rest mass energy used for ionization. The bounds for the Wilkinson microwave anisotropy probe (WMAP) 4y data are significantly lower, because of its lack of high S/N polarization measurements, but it can strongly constrain O (MeV) particles such as those proposed by Boehm et al. (2004).
Padmanabhan et al. (Tue,) studied this question.