Narrow-band parametrization for the stochastic gravitational wave background

In light of the nonperturbative resonance effects that may occur during inflation, we introduce a parametrization for the power spectrum of the stochastic gravitational wave background characterized by narrow-band amplification. We utilize the universal ${\Omega }_{\mathrm{GW}}\propto k^3$ infrared limit, applicable to a wide array of gravitational wave sources, to devise a robust yet straightforward parametrization optimized for Markov chain Monte Carlo analyses. This parametrization is demonstrated through select examples where its application is pertinent, and we discuss the advantages of this approach over traditional parametrizations for narrow-band scenarios. To evaluate the sensitivity of our proposed model parameters, we apply a mock likelihood based on the CMB-Stage4 data. Furthermore, we explicate the computational process for the mapping relationship between the foundational model parameters and our parametrized framework, using a two-field inflation model that resonantly amplifies gravitational waves as an example.