Constraints on reconstructed dark energy model from SN Ia and BAO/CMB observations

The motivation of the present work is to reconstruct a dark energy model through the {\it dimensionless dark energy function} $X(z)$, which is the dark energy density in units of its present value. In this paper, we have shown that a scalar field $\phi$ having a phenomenologically chosen $X(z)$ can give rise to a transition from a decelerated to an accelerated phase of expansion for the universe. We have examined the possibility of constraining various cosmological parameters (such as the deceleration parameter and the effective equation of state parameter) by comparing our theoretical model with the latest Type Ia Supernova (SN Ia), Baryon Acoustic Oscillations (BAO) and Cosmic Microwave Background (CMB) radiation observations. Using the joint analysis of the SN Ia+BAO/CMB dataset, we have also reconstructed the scalar potential from the parametrized $X(z)$. The relevant potential is found, which comes to be a polynomial in $\phi$. From our analysis, it has been found that the present model favors the standard $\Lambda$CDM model within $1\sigma$ confidence level.