Growth of perturbations in dark energy parametrization scenarios
  In this paper, we study the evolution of dark matter perturbations in the
linear regime by considering the possibility of dark energy perturbations. To
do this, two popular parameterizations, CPL and BA with same number of free
parameters and different redshift dependency have been considered. We integrate
the full relativistic equations to obtain the growth of matter fluctuations for
both clustering and smooth versions of CPL and BA dark energy. The growth rate
is larger (smaller) than the $\Lambda$CDM in the smooth cases when $w<-1$
($w>-1$) but the dark energy clustering gives a larger (smaller) growth index
when $w>-1$ ($w<-1$). We measure the relative difference of the growth rate
with respect to concordance $\Lambda$CDM and study how it changes depending on
the free parameters. Furthermore, it is found that the difference of growth
rates between smooth CPL and BA is negligible, less than $0.5\%$, while for
clustering case, the difference is considerable and might be as large as 2$\%$.
Eventually, using the latest geometrical and growth rate observational data, we
perform an overall likelihood analysis and show that both smooth and clustering
cases of CPL and BA parameterizations are consistent with observations. In
particular, we find the dark energy FoM $\sim70$ for the BA and $\sim30$ for
the CPL which indicates BA model constraints relatively better than CPL one.
