The present work is based on a parametric reconstruction of the deceleration parameter q(z) in a model for the spatially flat FRW universe filled with dark energy and non-relativistic matter. In cosmology, the parametric reconstruction technique deals with an attempt to build up a model by choosing some specific evolution scenario for a cosmological parameter and then estimate the values of the parameters with the help of different observational datasets. In this paper, we have proposed a logarithmic parametrization of q(z) to probe the evolution history of the universe. Using the type Ia supernova, baryon acoustic oscillation and the cosmic microwave background datasets, the constraints on the arbitrary model parameters q 0 and q 1 are obtained (within 1σ and 2σ confidence limits) by χ 2 -minimization technique. We have then reconstructed the deceleration parameter, the total EoS parameter ω tot , the jerk parameter and have compared the reconstructed results of q(z) with other well-known parametrizations of q(z). We have also shown that two model selection criteria (namely, the Akaike information criterion and Bayesian information criterion) provide a clear indication that our reconstructed model is well consistent with other popular models.

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 ω φ (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 [30]. 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 ω φ (z) and have found that the results are compatible with a ΛCDM universe if we consider SN Ia + Hubble data but inclusion of BAO/CMB data makes q(z) and ω φ (z) incompatible with ΛCDM model. The potential term for the present toy model is found to be functionally similar to a Higgs potential.

We study the accelerated expansion phase of the universe by using the kinematic approach. In particular, the deceleration parameter q is parametrized in a model-independent way. Considering a generalized parametrization for q, we first obtain the jerk parameter j (a dimensionless third time derivative of the scale factor) and then confront it with cosmic observations. We use the latest observational dataset of the Hubble parameter H(z) consisting of 41 data points in the redshift range of 0.07 ≤ z ≤ 2.36, larger than the redshift range that covered by the Type Ia supernova. We also acquire the current values of the deceleration parameter q0, jerk parameter j0 and transition redshift zt (at which the expansion of the universe switches from being decelerated to accelerated) with 1σ errors (68.3% confidence level). As a result, it is demonstrate that the universe is indeed undergoing an accelerated expansion phase following the decelerated one. This is consistent with the present observations. Moreover, we find the departure for the present model from the standard ΛCDM model according to the evolution of j. Furthermore, the evolution of the normalized Hubble parameter is shown for the present model and it is compared with the dataset of H(z).

The motivation of the present work is to reconstruct a dark energy model through the 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 φ 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, a polynomial in φ. From our analysis, it has been found that the present model favors the standard CDM model within 1σ confidence level.