Cosmology with decaying particles

We consider a cosmological model in which an unstable massive relic particle species (denoted by X) has an initial mass density relative to baryons β^-1{≡}ρX/ρB{}1, and then decays recently (red-shift z{}1000) into particles which are still relativistic today (denoted by R). We write down and solve the coupled equations for the cosmic scale factor a(t), the energy density in the various components (ρX,ρR,ρB), and the growth of linear density perturbations ({δ}{ρ}/{ρ}). The solutions form a one-parameter ({β}) family of solutions; physically β^-1{}(ΩR/Ω_NR)(1+zD) = (ratio today of energy density of relativistic to nonrelativistic particles)×{}(1+ red-shift of decay). We discuss the observational implications of such a cosmological model and compare our results to earlier results computed in ``the simultaneous decay approximation.'' In an appendix we briefly consider the case where one of the decay products of the X is massive and becomes nonrelativistic by the present epoch.