Reheating Dynamics in Inflationary Cosmology: Insights from $\alpha$-Attractor and $\alpha$-Starobinsky Models

Reheating in inflationary cosmology is essential for understanding the early universe, influencing particle production, thermalization, and the primordial power spectrum. Crucial quantities defined during the reheating epoc, such as the equation of state parameter $\omega_{re}$, reheating temperature $T_{re}$, and the number of $e$-folds $N_{re}$, affect inflationary observables like the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$. We analyze two classes of inflationary models: generalized $\alpha$-attractor models and the $\alpha$-Starobinsky generalization. These models, motivated by supergravity and string theory, exhibit attractor behavior, ensuring strong predictions and have been studied extensively before. A salient novelty of this study, compared to previous works, is the inclusion of an analytical expression for the reheating temperature, $T_{\text{re}}$, which makes it a dynamical quantity. This is crucial for determining all the cosmological quantities analyzed in this work. Our results show a universal scaling behavior for a tightly bounded $T_{re}$ in both models. We believe this is the first time that $T_{re}$ is so closely determined. This work complements previous Bayesian and numerical studies by providing detailed numerical and analytical insights into the evolution of cosmological observables and reheating parameters, offering also constraints on inflationary models based on observational data.