Constraints from the Wilkinson microwave anisotropy probe on decaying cold dark matter

We reformulate cosmological perturbations in the decaying cold dark matter model, and calculate cosmological microwave background anisotropies. By comparing our predictions with data from the Wilkinson Microwave Anisotropy Probe, we derive a new bound on the abundance and lifetime of decaying dark matter particles. The lifetime is constrained to Gamma(-1)greater than or equal to123 Gyr at 68% C.L. (52 Gyr at 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 generalizes to Omega(DDM)h(2)less than or similar to-0.5(Gamma(-1)/1 Gyr)(-1)+0.12 for Gamma(-1)greater than or equal to5 Gyr at 95.4% C.L.