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

Recent studies of the structures of galaxies and clusters imply that dark matter might be unstable and may decay with lifetime Gamma(-1), about the age of the 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 the 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 the power at small scale (l > 4000). This is in marked contrast with the dependence of other cosmological parameters such as the amplitude of mass fluctuations 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 separately. We also investigate the sensitivity of future SZ surveys to the cosmological parameters including the lifetime, assuming a fiducial model Gamma(-1) = 10 h(-1) 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 a factor of 2 even if sigma(8) and Omega(lambda) are marginalized.