Scalar Field and Quintessence in Late-Time Cosmic Expansion

The persistent Hubble tension—marked by a notable disparity between early- and late-universe determinations of the Hubble constant $H_0$—poses a serious challenge to the standard cosmological framework. Closely linked to this is the $H_0-r_d$ tension, which stems from the fact that BAO-based estimates of $H_0$ are intrinsically dependent on the assumed value of the sound horizon at the drag epoch, $r_d$. In this study, we construct a scalar field dark energy model within the framework of a spatially flat Friedmann–Lemaitre–Robertson–Walker model to explore the dynamics of cosmic acceleration. To solve the field equations, we introduce a generalized extension of the standard Lambda Cold Dark Matter model that allows for deviations in the expansion history. Employing advanced Markov Chain Monte Carlo techniques, we constrain the model parameters using a comprehensive combination of observational data, including Baryon Acoustic Oscillations, Cosmic Chronometers, and Standard Candle datasets from Pantheon, Quasars, and Gamma-Ray Bursts (GRBs). Our analysis reveals a transition redshift from deceleration to acceleration at $z_{\mathrm{tr}}=0.69$ and a present-day deceleration parameter value of $q_0=-0.64$. The model supports a dynamical scalar field interpretation, with an equation of state parameter satisfying $-1<{\omega }_0^{\varphi }<0$, consistent with quintessence behavior, and signaling a deviation from the $\Lambda$. While the model aligns closely with the Lambda Cold Dark Matter scenario at lower redshifts ($z\lesssim 0.65$), notable departures emerge at higher redshifts ($z\gtrsim 0.65$), offering a potential window into modified early-time cosmology. Furthermore, the evolution of key cosmographic quantities such as energy density ${\rho }^{\varphi }$, pressure $p^{\varphi }$, and the scalar field equation of state highlights the robustness of scalar field frameworks in describing dark energy phenomenology. Importantly, our results indicate a slightly higher value of the Hubble constant $H_0$ for specific data combinations, suggesting that the model may provide a partial resolution of the current $H_0$ tension.