Fractional Dark Matter decay: cosmological imprints and observational constraints

If a fraction f(dcdm) of the Dark Matter decays into invisible and massless particles (so-called "dark radiation") with the decay rate (or inverse lifetime) Gamma(dcdm), such decay will leave distinctive imprints on cosmological observables. With a full consideration of the Boltzmann hierarchy, we calculate the decay-induced impacts not only on the CMB but also on the redshift distortion and the kinetic Sunyaev-Zel'dovich effect, while providing detailed physical interpretations based on evaluating the evolution of gravitational potential. By using the current cosmological data with a combination of Planck 2015, Baryon Acoustic Oscillation and redshift distortion measurements which can improve the constraints, we update the 1 sigma bound on the fraction of decaying DM from f(dcdm). less than or similar to 5.26% to f(dcdm). less than or similar to 2.73% for the short-lived DM (assuming Gamma(dcdm)/H-0 greater than or similar to 10(4)). However, no constraints are improved from RSD data (f(dcdm) less than or similar to 0.94%) for the long-lived DM (i.e., Gamma(dcdm)/H-0 less than or similar to 10(4)). We also find the fractional DM decay can only slightly reduce the H-0 and sigma(8) tensions, which is consistent with other previous works. Furthermore, our calculations show that the kSZ effect in future would provide a further constraining power on the decaying DM.