In this paper we obtain observational constraints on three dynamical cold dark energy models , include PL , CPL and FSL , with most recent cosmological data and investigate their implication for structure formation , dark energy clustering and abundance of CMB local peaks .
From the joint analysis of the CMB temperature power spectrum from observation of the Planck , SNIa light-curve , baryon acoustic oscillation , f \sigma _ { 8 } for large scale structure observations and the Hubble parameter , we find that \Omega _ { DE } = 0.6862 \pm 0.0078 , \alpha = 0.1013 \pm 0.0031 and w _ { 0 } = -1.3799 ^ { +0.0036 } _ { -0.0028 } for the PL model , \Omega _ { DE } = 0.6880 ^ { +0.0100 } _ { -0.0079 } , w _ { 0 } = -1.08045 ^ { +0.00041 } _ { -0.00062 } and w _ { 1 } = -0.12190 ^ { +0.00050 } _ { -0.00030 } for the CPL model and \Omega _ { DE } = 0.6893 \pm 0.0078 , w _ { 0 } = -0.9994 \pm 0.0076 and w _ { 1 } = -0.0082 ^ { +0.0044 } _ { -0.0051 } for the FSL model at 1 \sigma confidence interval .
The PL model has matter-like contribution to the energy content of early universe due to crossing behavior of its Equation of state .
Therefore , the PL model has the highest growth of matter density , \Delta _ { m } , and matter power spectrum , P ( k ) , compared to \Lambda CDM and other models .
For the CPL on the other hand , the structure formation is considerably suppressed while the FSL has behavior similar to standard model of cosmology .
Studying the clustering of dark energy , \Delta _ { DE } , yields positive but small value with maximum of \Delta _ { DE } \simeq 10 ^ { -3 } at early time due to matter behaviour of the PL , while for the CPL and FSL cross \Delta _ { DE } = 0 several time which demonstrate void of dark energy with \Delta _ { DE } \simeq - 10 ^ { -11 } in certain periods of the history of dark energy evolution .
Among these three models , the PL model demonstrate that is more compatible with f \sigma _ { 8 } data .
We also investigated a certain geometrical measure , namely the abundance of local maxima as a function of threshold for three DDE models and find that the method is potentially capable to discriminate between the models , especially far from mean threshold .
The contribution of PL and CPL for late ISW are significant compared to cosmological constant and FSL model .
The tension in the Hubble parameters is almost alleviated in the PL model .