We propose a scenario where preheating occurs for a specific duration that is
parametrized by an e-folds number $N_{pre}$, our results suggest a direct
correlation between the preheating duration and the density of gravitational
waves (GWs) produced during this phase. Moreover, we investigate the
consequences of the inflationary parameters on the $\alpha$-attractor E model
in the small $\alpha$ limits. In this framework, we perform investigations on
the preheating parameters involving the number of e-folds $N_{pre}$, and the
temperature of reheating $T_{re}$, then we show that the parameter $n$
associated with the E model of $\alpha$-attractor inflation has a negligible
effect on the preheating duration, and we demonstrate that gravitational wave
generation during preheating satisfies the restrictions from Planck’s recent
data.
