This research explores the stability characteristics of a cosmological model constructed within the framework of scalar-tensor gravity, incorporating both theoretical derivations and numerical simulations. A variable deceleration parameter dependent on time is utilized to obtain explicit expressions for the scale factor, scalar field, pressure, and energy density. To examine the physical plausibility of the model, we conduct a linear perturbation study by introducing small deviations in matter and scalar field variables. Through the application of the growth rate parameter approach, the model displays a credible shift from early-time instability to a stable late-time cosmic behavior, aligning with the observed acceleration of the universe. The analytical outcomes are supported by numerical integration using the fourth-order Runge-Kutta algorithm, which confirms the damping of perturbations over time. Furthermore, the model’s compatibility with current observations is tested using the Maximum Likelihood Estimation technique, employing Hubble parameter datasets and the Pantheon sample of Type Ia supernovae. The close match between theoretical predictions and observational data affirms the robustness of the proposed scenario. Overall, the combined use of analytic modeling, computational methods, and statistical comparison indicates that the scalar-tensor theory, when paired with the selected deceleration parameter, offers a reliable and observationally consistent representation of cosmic evolution.
Jain et al. (Fri,) studied this question.