  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.
