WMAP Constraints on Decaying Cold Dark Matter

We re-formulate cosmological perturbations in the decaying cold dark matter model, and calculate cosmological microwave background (CMB) anisotropies. By comparing our theoretical predictions with recent observational data from the Wilkinson Microwave Anisotropy Probe(WMAP), we derive a new bound on the abundance and lifetime of decaying dark matter particles. We show that the data of WMAP alone do not prefer the decaying cold dark matter model: the lifetime is constrained to \Gamma^{-1}> 123 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 in which cold dark matter consists of both stable and decaying particles, and show that the constraint generalizes down to \Omega_{DDM}h^2 < -0.5 (Gamma^{-1}/1 Gyr)^{-1}+0.12 for \Gamma^{-1} > 5 Gyr at 95.4% C.L.. These bounds are robust and widely applicable, because they are derived only from gravitational effects and therefore do not rely on the details of decay channels or decay products.