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, $10^{-4}Mp{c}^{-1}$ to $1Mp{c}^{-1}$ 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: $\widehat{n_t}(f)$ 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 $\hat{w}(f)$, $\widehat{n_t}(f)$ 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.

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