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 FLRW model to explore the dynamics of cosmic acceleration. To solve the field equations, we introduce a generalized extension of the standard ΛCDM 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 Type Ia Supernovae (SNe Ia), Quasars, and Gamma-Ray Bursts (GRBs). Our analysis reveals a transition redshift from deceleration to acceleration at \( z_{tr} = 0.69 \), 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 \( −1 < ω_ϕ 0 < 0 \), consistent with quintessence behavior, and signaling a deviation from the cosmological constant. While the model aligns closely with the ΛCDM scenario at lower redshifts (z ≲ 0.65), notable departures emerge at higher redshifts (z ≳ 0.65), offering a potential window into modified early-time cosmology. Furthermore, the evolution of key cosmographic quantities such as energy density \( ρ_ϕ \), pressure \( p_ϕ \), 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.