We present a comprehensive analysis of the preheating dynamics and associated gravitational wave signatures in the Higgs-$R^2$ inflationary model. Using lattice simulations, we investigate the postinflationary evolution of the system across the parameter space, covering both the Higgs-like and $R^2$-like scenarios. We demonstrate that the efficiency of preheating is significantly dependent on the nonminimal coupling parameter $\xi$. As the $\xi$ parameter increases, moving from the $R^2$-like regime to the Higgs-like regime, we observe more efficient preheating. Through detailed numerical computations, efficient preheating is shown to lead to stronger gravitational wave production. The amplitude of the gravitational wave spectrum varies by several orders of magnitude as we move from the $R^2$-like regime to the Higgs-like regime. The resultant gravitational wave signatures can serve as a potential observational probe to distinguish between different parameter regimes of the Higgs-$R^2$ model.

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• Cosmology
• Gravitational waves
• Inflation