This article discusses a dark energy cosmological model in the standard theory of gravity - general relativity with a broad scalar field as a source. Exact solutions of Einstein’s field equations are derived by considering a particular form of deceleration parameter $q$, which shows a smooth transition from decelerated to accelerated phase in the evolution of the universe. The external datasets such as Hubble ($H\left(z\right)$) datasets, Supernovae (SN) datasets, and Baryonic Acoustic Oscillation (BAO) datasets are used for constraining the model par parameters appearing in the functional form of $q$. The transition redshift is obtained at $z_t=0.67_{-0.36}^{+0.26}$ for the combined dataset ($H\left(z\right)+SN+BAO$), where the model shows signature-flipping and is consistent with recent observations. Moreover, the present value of the deceleration parameter comes out to be $q_0=-0.50_{-0.11}^{+0.12}$ and the jerk parameter $j_0=-0.98_{-0.02}^{+0.06}$ (close to 1) for the combined datasets, which is compatible as per Planck2018 results. The analysis also constrains the omega value i.e., ${\Omega }_{m_0}\le 0.269$ for the smooth evolution of the scalar field EoS parameter. It is seen that energy density is higher for the effective energy density of the matter field than energy density in the presence of a scalar field. The evolution of the physical and geometrical parameters is discussed in some details with the model parameters’ numerical constrained values. Moreover, we have performed the state-finder analysis to investigate the nature of dark energy.

本文讨论了标准引力理论中的暗能量宇宙学模型-广义相对论，以宽标量场为源。爱因斯坦场方程的精确解是通过考虑特殊形式的减速参数得出的$q$，它显示了宇宙演化中从减速到加速阶段的平稳过渡。外部数据集，例如Hubble（$H（ž）$）数据集，超新星（SN）数据集和重子声振荡（BAO）数据集用于约束以函数形式出现的模型par参数。 $q$。在以下位置获得过渡红移${ž}_{Ť}=0。67_{-0。36}^{+0。26}$ 对于组合的数据集（$H（ž）+\mathrm{小号}ñ+乙\mathrm{一个}Ø$），其中模型显示签名翻转，并且与最近的观察结果一致。而且，减速参数的当前值变为$q_0=-0。50_{-0。11}^{+0。12}$ 和混蛋参数 ${Ĵ}_0=-0。98_{-0。02}^{+0。06}$（接近1）用于组合数据集，与Planck2018结果兼容。分析还限制了欧米茄值，即${\Omega }_{{米}_0}\le 0。269$标量场EoS参数的平滑演化。可以看出，物质场的有效能量密度的能量密度高于标量场存在下的能量密度。通过模型参数的数值约束值，详细讨论了物理和几何参数的演变。此外，我们已经进行了状态查找器分析，以研究暗能量的性质。