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In this study, we explore the enigma of late-time cosmic acceleration in the framework of a general scalar field playing the role of dark energy. Our investigation yields an exact solution to Einstein's field equations, achieved through a parametrization of the deceleration parameter q (a) in quadratic form in the homogeneous and isotropic background geometry represented by Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. This parametrization unveils a seamless transition from a decelerated to an accelerated phase in the cosmic evolution. Furthermore, we leverage this parametrization to reconstruct cosmological parameters with respect to redshift z, elucidating their dependency on certain model parameters that govern the universe's evolutionary trajectory. The model parameters are subsequently constrained using diverse observational datasets. We provide a comprehensive analysis of the evolution of geometrical and physical parameters, complete with the numerically constrained values. To gain deeper insights into the nature of dark energy, we employ Statefinder diagnostics, conducting a thorough examination. Our findings shed light on the intricate interplay between cosmic acceleration, quintessential dark energy and the parametrization of deceleration parameter, offering valuable insights into the fundamental dynamics of the universe. [ABSTRACT FROM AUTHOR]

In this paper, we are going to study quintom dark energy cosmological model. In that case we introduce the action of gravity which is minimally couple to scalar field ϕ and σ with potential V (ϕ , σ) . First we write the Lagrangian of corresponding model in FRW model. Here we also introduce the non-commutative geometry and modify the above model. The deformed model leads us to obtain the equation of state. And finally we discus the present cosmological in case of phantom and quintessence. And also, we investigate the critical point and stability of system. [ABSTRACT FROM AUTHOR]