We study gravitational wave production in an expanding Universe during the first stages following inflation, and investigate the consequences of the Gauss–Bonnet term on the inflationary parameters for a power-law inflation model with a GB coupling term. Moreover, we perform the analyses on the preheating parameters involving the number of e-folds $$N_{pre}$$ N pre , and the temperature of thermalization $$T_{th},$$ T th , and show that it’s sensitive to the parameters n, and $$\gamma $$ γ , the parameter $$\gamma $$ γ is proposed to connect the density energy at the end of inflation to the preheating energy density. We set a correlation of gravitational wave energy density spectrum with the spectral index $$n_{s}$$ n s detected by the cosmic microwave background experiments. The density spectrum $$\varOmega _{gw}$$ Ω gw shows good consistency with observation for $$\gamma =$$ γ = $$10^{3}$$ 10 3 and $$10^{6}$$ 10 6 . Our findings suggest that the generation of gravitational waves (GWs) during preheating can satisfy the constraints from Planck’s data.

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