$\Lambda$CDM-like models with future singularities

Abstract

We consider new models of dark energy with finite time future singularities, by introducing the pressure density as a function of the scale factor. This approach gives acceptable phenomenological models of dark energy, practically indistinguishable from the cosmological constant up to the present, which face future singularities at finite time and finite scale factor. Exact scalar field model representation was found for quintessence, Big Rip and type III singularity models. The simple form of the equation of state allows to establish a relationship between its current value, $w_0$, and the time or redshift at which the singularity takes place. The effect on the growth of matter perturbations was calculated.