Decaying dark matter mimicking time-varying dark energy

Abstract

A $\Lambda$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, ${\tilde{w}}_{\varphi }$, as a function of redshift, and show that the evolution of ${\tilde{w}}_{\varphi }$ 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 (${\tilde{w}}_{\varphi }>-1$), phantom models (${\tilde{w}}_{\varphi }<-1$) or models in which the equation of state parameter crosses the phantom divide, evolving from ${\tilde{w}}_{\varphi }>-1$ at high redshift to ${\tilde{w}}_{\varphi }<-1$ at low redshift. All of these models generically converge toward ${\tilde{w}}_{\varphi }\approx -1$ at the present. The degeneracy between the $\Lambda$CDM model with decaying dark matter and the corresponding spurious quintessence model is broken by the growth of density perturbations.

6 pages, 2 figures. Added discussion of linear perturbation growth - version accepted at PRD

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