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Decaying dark matter mimicking time-varying dark energy

A $Λ$CDM model with dark matter that decays into inert relativistic energy on a timescale longer than the Hubble time will produce an expansion history that can be misinterpreted as stable dark matter with time-varying dark energy. We calculate the corresponding spurious equation of state parameter, $\widetilde w_ϕ$, as a function of redshift, and show that the evolution of $\widetilde w_ϕ$ depends strongly on the assumed value of the dark matter density, erroneously taken to scale as $a^{-3}$. Depending on the latter, one can obtain models that mimic quintessence ($\widetilde w_ϕ> -1$), phantom models ($\widetilde w_ϕ< -1$) or models in which the equation of state parameter crosses the phantom divide, evolving from $\widetilde w_ϕ> -1$ at high redshift to $\widetilde w_ϕ< -1$ at low redshift. All of these models generically converge toward $\widetilde w_ϕ\approx -1$ at the present. The degeneracy between the $Λ$CDM model with decaying dark matter and the corresponding spurious quintessence model is broken by the growth of density perturbations.