  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.
