Evolution of matter perturbations in the context of cosmic slowing down

We investigate dynamical, time-evolving dark-energy models exhibiting phantom behaviour within Einstein gravity by analysing the evolution of matter perturbations. In particular, we consider five dark-energy parameterisations that predict a slowing down of the current cosmic acceleration. We examine the evolution of the growth index and its first derivative, as well as the combination parameter and the statefinder diagnostics, and compare their behaviour with that of the concordance $\Lambda$CDM model. For the parameter choices considered, the present-day values of the growth index and its first derivative are found to be compatible with ranges reported in previous phenomenological studies. The combination parameter is also found to differ from its $\Lambda$CDM value, while the statefinder parameters provide additional means of distinguishing the considered dynamical dark-energy scenarios from the concordance model. Our results illustrate the phenomenological signatures associated with these models and identify observables that may be useful for future observational tests. We stress, however, that the present analysis does not constitute a statistical model comparison or establish an observational preference for any of the considered dynamical dark-energy models over $\Lambda$CDM.