Gravitational wave production after inflation for a hybrid inflationary model

Abstract: We discuss a cosmological scenario with a stochastic background of gravitational waves sourced by the tensor perturbation due to a hybrid inflationary model with cubic potential. The tensor-to-scalar ratio for the present hybrid inflationary model is obtained as $r \approx 0.0006$. Gravitational wave spectrum of this stochastic background, for large-scale CMB modes, $10^{-4}Mpc^{-1}$ to $1Mpc^{-1}$ is studied. The present-day energy spectrum of gravitational waves $\Omega_0^{gw}(f)$ is sensitively related to the tensor power spectrum and r which is, in turn, dependent on the unknown physics of the early cosmos. This uncertainty is characterized by two parameters: $\hat{n_t}(f)$ logarithmic average over the primordial tensor spectral index and $\hat{w}(f)$ logarithmic average over the effective equation of state parameter. Thus, exact constraints in the $\hat{w}(f)$, $\hat{n_t}(f)$ plane can be obtained by comparing theoretical constraints of our model on r and $\Omega_0^{gw}(f)$. We obtain a limit on $\hat{w}(10^{-15}Hz)$<$0.33$ around the modes probed by CMB scales.