Scalar Field Cosmology with Logarithmic Deceleration Parameter

In this study, we present an alternative framework for understanding the dynamics of late-time cosmic acceleration. Central to our research is a specific methodology for modeling the expansion history of the universe and the nature of dark energy by a logarithmic parametrization of the deceleration parameter q(z). This specific form facilitates a model-independent reconstruction of the expansion history, allowing the cosmic evolution to be determined empirically, yet it remains fully consistent with scalar-field-driven dark energy models within the framework of General Relativity.

Our theoretical structure is built upon Scalar Field Cosmology, where cosmic dynamics are governed by a minimally coupled scalar field (ϕ) possessing a generalized potential V(ϕ). This potential is meticulously designed to coherently reproduce the observed late-time acceleration phase of the universe. The logarithmic form of q(z) allows for the reconstruction of all fundamental dynamic quantities in a closed analytical form. This analytical tractability is crucial for theoretical analysis and direct comparison with observations.

To constrain the model’s free parameters, we utilized a robust and extensive set of observational data. This includes Cosmic Chronometers (CCs), high-precision Standard Candle (SC) observations from Type Ia Supernovae (specifically the Pantheon+ sample), Baryon Acoustic Oscillation (BAO) data, and the strong constraint provided by the R19 local Hubble constant prior. All datasets were meticulously combined and analyzed through a combined χ^2 minimization procedure, ensuring the maximization of the model’s observational consistency and statistical power.

The results unequivocally demonstrate a clear evolutionary transition from a past decelerating phase to the current accelerating phase. The reconstructed transition redshift (z_t) is found to lie within the interval z_t ≈ 0.70–0.90, which is remarkably consistent with modern cosmological findings. The high degree of consistency between our model and the observational data proves that the logarithmic deceleration mechanism can provide a successful explanation for the universe's evolution.