A new parametrization of dark energy equation of state leading to double
  exponential potential
  We show that a canonical scalar field with a phenomenological form of energy
density or equivalently an equation of state parameter can provide the required
transition from decelerated ($q>0$) to accelerated expansion ($q<0$) phase of
the universe. We have used the latest Type Ia Supernova (SNIa) and Hubble
parameter datasets to constrain the model parameters. It has been found that
for each of these dataset, the transition in deceleration parameter $q$ takes
place at the recent past ($z<1$). The future evolution of $q$ is also discussed
in the context of the model under consideration. Furthermore, using those
datasets, we have reconstructed $\omega_{\phi}(z)$, the equation of state
parameter for the scalar field. The results show that the reconstructed forms
of $q(z)$ and $\omega_{\phi}(z)$ do not differ much from the standard
$\Lambda$CDM value at the current epoch. Finally, the functional form of the
relevant potential $V(\phi)$ is derived by a parametric reconstruction from the
observational dataset. The corresponding $V(\phi)$ comes out to be a double
exponential potential which has a number of cosmological implications.
Additionally, we have also studied the effect of this particular scalar field
dark energy sector on the evolution of matter over-densities and compared it
with the $\Lambda$CDM model.
