  We carry out an analysis of the cosmological perturbations in general
relativity for three different models which are good candidates to describe the
current acceleration of the Universe. These three set-ups are described
classically by perfect fluids with a phantom nature and represent deviations
from the most widely accepted $\Lambda$CDM model. In addition, each of the
models under study induce different future singularities or abrupt events known
as (i) Big Rip, (ii) Little Rip and (iii) Little Sibling of the Big Rip. Only
the first one is regarded as a true singularity since it occurs at a finite
cosmic time. For this reason, we refer to the others as abrupt events. With the
aim to find possible footprints of this scenario in the Universe matter
distribution, we not only obtain the evolution of the cosmological scalar
perturbations but also calculate the matter power spectrum for each model. We
have carried the perturbations in the absence of any anisotropic stress and
within a phenomenological approach for the speed of sound. We constrain
observationally these models using several measurements of the growth rate
function, more precisely $f\sigma_8$, and compare our results with the
observational ones.
