Sunyaev-Zel'dovich power spectrum with decaying cold dark matter

Recent studies of structures of galaxies and clusters imply that dark matter might be unstable and decay with lifetime $\Gamma^{-1}$ about the age of universe. We study the effects of the decay of cold dark matter on the Sunyaev-Zel'dovich (SZ) power spectrum. We analytically calculate the SZ power spectrum taking finite lifetime of cold dark matter into account. We find the finite lifetime of dark matter decreases the power at large scale ($l < 4000$) and increases at small scale ($l > 4000$). This is in marked contrast with the dependence of other cosmological parameters such as the amplitude of mass fluctuations $\sigma_{8}$ and the cosmological constant $\Omega_{\lambda}$ (under the assumption of a flat universe) which mainly change the normalization of the angular power spectrum. This difference allows one to determine the lifetime and other cosmological parameters rather separately. We also investigate sensitivity of a future SZ survey to the cosmological parameters including the life time, assuming a fiducial model $\Gamma^{-1} = 10 h^{-1} {\rm Gyr}$, $\sigma_{8} = 1.0$, and $\Omega_{\lambda} = 0.7$. We show that future SZ surveys such as ACT, AMIBA, and BOLOCAM can determine the lifetime within factor of two even if $\sigma_{8}$ and $\Omega_{\lambda}$ are marginalized.