A new parametrization of dark energy equation of state leading to double exponential potential

Abstract: 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.