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 (zt) is found to lie within the interval zt ≈ 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.
I have a question regarding the logarithmic parametrization of the deceleration parameter q(z).
Since the deceleration parameter is directly determined by the Hubble parameter and its derivative, could you clarify what motivated the specific logarithmic form?
Is there a physical justification for this choice, or was it mainly selected for analytical tractability?
Additionally, would parametrizing the Hubble parameter itself lead to qualitatively different constraints?
Thank you for your question regarding our work. Here is a concise clarification of our choice:
1) The selection of the logarithmic parametrization $q(z) = q_0 + q_1 \ln(1+z)$ was primarily driven by:
• This specific form facilitates the reconstruction of expansion history, including the Hubble parameter $H(z)$ and scalar potential $V(\phi)$, in a closed analytical form.
• It allows the cosmic evolution to be determined empirically from observational data rather than relying on a fixed cosmological constant.
• It successfully captures the phase transition from deceleration to acceleration at a precise redshift of $z_{tr} \approx 0.785$, which aligns with modern cosmological findings.
2) While one could parametrize $H(z)$ directly, our approach focusing on $q(z)$ provides specific advantages:
• Our model yields an intermediate value of $H_0 = 71.41 \pm 0.98$ km/s/Mpc, offering a potential pathway to alleviate the current Hubble tension.
• This method reveals a dynamic equation of state $\omega_{\phi}(z)$ that distinguishes itself from a static $\Lambda$, providing deeper insight into the scalar field's nature.
In short, the logarithmic form was chosen because it bridges the gap between theoretical tractability and physical viability.
