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

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