A divergence free parametrization of deceleration parameter for scalar field dark energy

In this paper, we have considered a spatially flat FRW universe filled with pressureless matter and dark energy. We have considered a phenomenological parametrization of the deceleration parameter $q(z)$ and from this we have reconstructed the equation of state for dark energy ${\omega }_{\varphi }(z)$. This divergence free parametrization of the deceleration parameter is inspired from one of the most popular parametrization of the dark energy equation of state given by Barboza and Alcaniz. Using the combination of datasets (SN Ia $+$ Hubble $+$ BAO/CMB), we have constrained the transition redshift $z_t$ (at which the universe switches from a decelerating to an accelerating phase) and have found the best fit value of $z_t$. We have also compared the reconstructed results of $q(z)$ and ${\omega }_{\varphi }(z)$ and have found that the results are compatible with a $\mathrm{\Lambda }$CDM universe if we consider SN Ia $+$ Hubble data but inclusion of BAO/CMB data makes $q(z)$ and ${\omega }_{\varphi }(z)$ incompatible with $\mathrm{\Lambda }$CDM model. The potential term for the present toy model is found to be functionally similar to a Higgs potential.