Constraints from the Wilkinson Microwave Anisotropy Probe on DecayingCold Dark Matter

We reformulate cosmological perturbations in the decaying cold dark mattermodel, and calculate cosmological microwave background anisotropies. By comparingour predictions with data from the Wilkinson Microwave Anisotropy Probe, wederive a new bound on the abundance and lifetime of decaying dark matter particles.The lifetime is constrained to Γ^-1≥123 Gyr at 68% C.L. (52 Gyrat 95.4% C.L.) when cold dark matter consists only of such decaying particles.We also consider a more general case and show that the constraint generalizesto ${{Ω}}DDM{h}²{}{-}0.5({{Γ}}^{{-}1}/1 Gyr{)}^{{-}1}+0.12$ for ${{Γ}}^{{-}1}{≥}5 Gyr$ at 95.4% C.L.