Study of parametrized dark energy models with a general non-canonical scalar field

In this paper, we have considered various dark energy models in the framework of a non-canonical scalar field with a Lagrangian density of the form ${\cal L}(\phi, X)=f(\phi)X{\left(\frac{X}{M^{4}_{Pl}}\right)}^{\alpha -1} - V(\phi)$, which provides the standard canonical scalar field model for $\alpha=1$ and $f(\phi)=1$. In this particular non-canonical scalar field model, we have carried out the analysis for $\alpha=2$. We have then obtained cosmological solutions for constant as well as variable equation of state parameter ($\omega_{\phi}(z)$) for dark energy. We have also performed the data analysis for three different functional forms of $\omega_{\phi}(z)$ by using the combination of SN Ia, BAO and CMB datasets. We have found that for all the choices of $\omega_{\phi}(z)$, the SN Ia $+$ CMB/BAO dataset favors the past decelerated and recent accelerated expansion phase of the universe. Furthermore, using the combined dataset, we have observed that the reconstructed results of $\omega_{\phi}(z)$ and $q(z)$ are almost choice independent and the resulting cosmological scenarios are in good agreement with the $\Lambda$CDM model (within the $1\sigma$ confidence contour). We have also derived the form of the potentials for each model and the resulting potentials are found to be a quartic potential for constant $\omega_{\phi}$ and a polynomial in $\phi$ for variable $\omega_{\phi}$.