Preheating constraints in ?-attractor inflation and gravitational waves production

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