Dark energy and dark matter perturbations in singular universes

We discuss the evolution of density perturbations of dark matter and dark energy in cosmological models which admit future singularities in a finite time. Up to now geometrical tests of the evolution of the universe do not differentiate between singular universes and $\mathrm{\Lambda }$CDM scenario. We solve perturbation equations using the gauge invariant formalism. The analysis shows that the detailed reconstruction of the evolution of perturbations within singular cosmologies, in the dark sector, exhibit important differences between the singular universes models and the $\mathrm{\Lambda }$CDM cosmology. This is encouraging for further examination and gives hope for discriminating between those models with future galaxy weak lensing experiments like the Dark Energy Survey (DES) and Euclid or CMB observations like PRISM and CoRE.