Dark matter ( DM ) annihilation during hydrogen recombination ( z \sim 1000 ) 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 \epsilon _ { dm } , 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 \epsilon _ { dm } ( z = 1000 ) > 10 ^ { -15 } { ~ { } eV } / { s } / { proton } , while high sensitivity experiments ( eg .
NASA ’ s CMBPOL ) could improve that constraint to \epsilon _ { dm } ( z = 1000 ) > 4 \times 10 ^ { -16 } { ~ { } eV } / { s } / { proton } , assuming a fractional detector sensitivity of \Delta T / T \sim 1 \mu { K } and a beam of 3 ^ { \prime } .
These limits translate into a lower bound on the mass of the DM particle , M _ { dm } > 10 ~ { } - ~ { } 100 { ~ { } GeV } , assuming a single species with a cross section of \langle \sigma _ { A } v \rangle \sim 2 \times 10 ^ { -26 } { ~ { } cm } ^ { 3 } / { s } , and a fraction f \sim 0.1 ~ { } - ~ { } 1 of the rest mass energy used for ionization .
The bounds for the WMAP 4y data are significantly lower , because of its lack of high S/N polarization measurements , but it can strongly constrain { \cal O } ( { ~ { } MeV } ) particles such as those proposed by Boehm et al ( 2004 ) .